111 + Interview Questions in The Foundation: Logics And Proofs in Discrete Mathematics Page 1 InterviewSolution

1.	A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as ___________(a) Direct proof(b) Contrapositive proofs(c) Vacuous proof(d) Proof by casesThis question was addressed to me in my homework.I want to ask this question from Types of Proofs in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» RIGHT answer is (C) Vacuous proof Best EXPLANATION: Definition of proof by CASES.

Discussion

2.	Which of the arguments is not valid in proving sum of two odd number is not odd.(a) 3 + 3 = 6, hence true for all(b) 2n +1 + 2m +1 = 2(n+m+1) hence true for all(c) All of the mentioned(d) None of the mentionedThe question was asked in a job interview.This question is from Types of Proofs topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct option is (a) 3 + 3 = 6, hence true for all The EXPLANATION is: Some EXAMPLES are not valid in proving RESULTS.

Discussion

3.	A theorem used to prove other theorems is known as _______________(a) Lemma(b) Corollary(c) Conjecture(d) None of the mentionedI have been asked this question in an online quiz.This question is from Types of Proofs in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT OPTION is (a) LEMMA Best EXPLANATION: DEFINITION of lemma.

Discussion

4.	A proof that p → q is true based on the fact that q is true, such proofs are known as ___________(a) Direct proof(b) Contrapositive proofs(c) Trivial proof(d) Proof by casesI have been asked this question in class test.This interesting question is from Types of Proofs in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT OPTION is (c) Trivial PROOF The best EXPLANATION: Definition of trivial proof.

Discussion

5.	A proof covering all the possible cases, such type of proofs are known as ___________(a) Direct proof(b) Proof by Contradiction(c) Vacuous proof(d) Exhaustive proofThe question was posed to me in examination.This interesting question is from Types of Proofs topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT ANSWER is (d) Exhaustive proof The BEST explanation: DEFINITION of exhaustive proof.

Discussion

6.	In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?(a) Direct proof(b) Proof by Contradiction(c) Vacuous proof(d) Mathematical InductionThis question was posed to me in class test.This key question is from Types of Proofs in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT answer is (b) PROOF by CONTRADICTION Easiest explanation: DEFINITION of proof by contradiction.

Discussion

7.	Let the statement be “If n is not an odd integer then sum of n withsome notodd numberwill not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some notodd number will not be odd.” A proof by contraposition will be ________(a) ∀nP ((n) → Q(n))(b) ∃ nP ((n) → Q(n))(c) ∀n~(P ((n)) → Q(n))(d) ∀n(~Q ((n)) → ~(P(n)))This question was addressed to me in class test.This intriguing question comes from Types of Proofs topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right answer is (d) ∀N(~Q ((n)) → ~(P(n))) Explanation: Definition of proof by CONTRAPOSITION.

Discussion

8.	When to proof P→Q true, we proof P false, that type of proof is known as ___________(a) Direct proof(b) Contrapositive proofs(c) Vacuous proof(d) Mathematical InductionI have been asked this question at a job interview.Enquiry is from Types of Proofs topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right ANSWER is (C) VACUOUS PROOF Explanation: Definition of vacuous proof.

Discussion

9.	Let the statement be “If n is not an odd integer then square of n is notodd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove _________(a) ∀nP ((n) → Q(n))(b) ∃ nP ((n) → Q(n))(c) ∀n~(P ((n)) → Q(n))(d) ∀nP ((n) → ~(Q(n)))The question was posed to me in semester exam.My enquiry is from Types of Proofs in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» RIGHT answer is (a) ∀nP ((n) → Q(n)) For explanation: Definition of DIRECT proof.

Discussion

10.	Which of the following can only be used in disproving the statements?(a) Direct proof(b) Contrapositive proofs(c) Counter Example(d) Mathematical InductionThe question was posed to me at a job interview.The question is from Types of Proofs topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right choice is (C) COUNTER Example Explanation: Counter EXAMPLES cannot be used to PROVE results.

Discussion

11.	“Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that __________(a) Parul is out for trip(b) Raju is playing chess(c) Parul is out for a trip and Raju is playing chess(d) Parul is out for a trip or Raju is playing chessI have been asked this question in semester exam.The above asked question is from Logics topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct CHOICE is (d) Parul is out for a trip or Raju is playing chess For EXPLANATION I WOULD say: LET P be “It is snowing,” q be “Parul is out for a trip,” and r the proposition “Raju is playing chess.” The hypotheses as ¬p ∨ q and p ∨ r, respectively. Using resolution, the proposition q ∨ r is, “Parul is out for a trip or Raju is playing chess.”

Discussion

12.	Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”(a) Modus tollens(b) Conjunction(c) Hypothetical syllogism(d) SimplificationI have been asked this question in final exam.Question is from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» RIGHT OPTION is (a) Modus tollens The EXPLANATION is: (¬N ∧ (M → N)) → ¬M is Modus tollens.

Discussion

13.	The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?(a) p ∨ r(b) p ∨ s(c) p ∨ q(d) q ∨ rThe question was asked during an online interview.I would like to ask this question from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT answer is (B) p ∨ s The explanation: The PREMISES (p ∧ q) ∨ r has two clauses: p ∨ r, and q ∨ r. We can also REPLACE r → s with the equivalent clause r ∨ s. Using the two clauses p ∨ r and r ∨ s, we can conclude p ∨ s.

Discussion

14.	Which rule of inference is used, ”Bhavika will work in an enterprise this summer. Therefore, this summer Bhavika will work in an enterprise or he will go to beach.”(a) Simplification(b) Conjunction(c) Addition(d) Disjunctive syllogismI had been asked this question in semester exam.My question is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct answer is (c) Addition For EXPLANATION I WOULD SAY: P → (p ∨ q) ARGUMENT is ‘Addition’.

Discussion

15.	Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”(a) Modus tollens(b) Modus ponens(c) Disjunctive syllogism(d) SimplificationI have been asked this question in class test.The above asked question is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct CHOICE is (B) MODUS ponens Best explanation: (M ∧ (M → N)) → N is Modus ponens.

Discussion

16.	Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers.(a) x = -1, y = 17(b) x = -2y = 8(c) Both x = -1, y = 17 and x = -2y = 8(d) Does not have any counter exampleThe question was posed to me in an online quiz.I need to ask this question from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT choice is (c) Both X = -1, y = 17 and x = -2y = 8 For explanation: Putting x=-1, y=17; -17>17 which is wrong. Putting x=-2, y=8; -16>8 which is wrong.

Discussion

17.	Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers.(a) True(b) FalseThe question was posed to me at a job interview.My doubt stems from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right option is (B) False Explanation: The equation does not SATISFY any value of m and n in the DOMAIN CONSIST of integers.

Discussion

18.	Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.”(a) ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures(b) ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class(c) ∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures(d) ∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lecturesThe question was posed to me during an online interview.I want to ask this question from Logics in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct choice is (a) ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the DOMAIN for x CONSISTS of all pupil in this CLASS, and the domain for y consists of all Discrete Maths lectures To elaborate: For some x pupil, there exists a course in Discrete Maths such that x has taken y.

Discussion

19.	Express, “The difference of a real number and itself is zero” using required operators.(a) ∀x(x − x! = 0)(b) ∀x(x − x = 0)(c) ∀x∀y(x − y = 0)(d) ∃x(x − x = 0)The question was asked in a national level competition.Enquiry is from Logics topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT choice is (B) ∀x(x − x = 0) To explain I would SAY: For every REAL number x, difference with itself is always zero.

Discussion

20.	Let T (x, y) mean that student x likes dish y, where the domain for x consists of all students at your school and the domain for y consists of all dishes. Express ¬T (Amit, South Indian) by a simple English sentence.(a) All students does not like South Indian dishes.(b) Amit does not like South Indian people.(c) Amit does not like South Indian dishes.(d) Amit does not like some dishes.I got this question in an internship interview.My question is based upon Logics in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct ANSWER is (d) Amit does not like some DISHES. The explanation: Negation of the STATEMENT Amit like SOUTH Indian dishes.

Discussion

21.	Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world.Use quantifiers to express, “Joy is loved by everyone.”(a) ∀x L(x, Joy)(b) ∀y L(Joy,y)(c) ∃y∀x L(x, y)(d) ∃x ¬L(Joy, x)I had been asked this question by my college professor while I was bunking the class.This interesting question is from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT option is (a) ∀X L(x, JOY) EASIEST explanation: Joy is loved by all the people in the WORLD.

Discussion

22.	Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).(a) True(b) FalseThis question was posed to me during an internship interview.This intriguing question comes from Logics topic in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer»

Discussion

23.	“The product of two negative real numbers is not negative.” Is given by?(a) ∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))(b) ∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))(c) ∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))(d) ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))This question was posed to me in an online quiz.Question is taken from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right choice is (d) ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0)) Explanation: For EVERY negative real NUMBER x and y, the product of these INTEGER is positive.

Discussion

24.	Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.(a) For all real number x there exists a real number y such that x is less than y(b) For every real number y there exists a real number x such that x is less than y(c) For some real number x there exists a real number y such that x is less than y(d) For each and everyreal number x and y such that x is less than yThis question was posed to me during a job interview.Question is taken from Logics in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT choice is (a) For all real NUMBER x there EXISTS a real number y such that x is less than y The best explanation: Statement is x is less than y. Quantifier USED are for each x, there exists a y.

Discussion

25.	Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers.(a) True(b) FalseThis question was addressed to me in an interview.My doubt is from Predicate Logic Quantifiers topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» RIGHT OPTION is (a) TRUE The EXPLANATION: For n=0, 4n=3n HENCE, it is true.

Discussion

26.	Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A).(a) True(b) FalseI got this question in unit test.I want to ask this question from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right OPTION is (b) False To elaborate: For each A there exist only ONE M, because there is no REAL number A such that M + A = 0 for all real NUMBERS M.

Discussion

27.	Let domain of m includes all students, P (m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English.(a) A student is there who spends more than 2 hours in playing polo(b) There is a student who does not spend more than 2 hours in playing polo(c) All students spends more than 2 hours in playing polo(d) No student spends more than 2 hours in playing poloI had been asked this question in homework.My doubt stems from Predicate Logic Quantifiers in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right ANSWER is (d) No student SPENDS more than 2 HOURS in PLAYING POLO Explanation: There is no student who spends more than 2 hours in playing polo.

Discussion

28.	”Everyone wants to learn cosmology.” This argument may be true for which domains?(a) All students in your cosmology class(b) All the cosmology learning students in the world(c) Both of the mentioned(d) None of the mentionedI had been asked this question in exam.The query is from Predicate Logic Quantifiers topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Right option is (C) Both of the mentioned The EXPLANATION is: Domain may be limited to your CLASS or may be whole WORLD both are good as it satisfies universal QUANTIFIER.

Discussion

29.	The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.(a) ∀x (F (x) → P (x))(b) ∀x (F (x) ∧ P (x))(c) ∃x (F (x) ∧ P (x))(d) ∃x (F (x) → P (x))The question was posed to me in class test.I'm obligated to ask this question of Predicate Logic Quantifiers in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» RIGHT ANSWER is (c) ∃x (F (x) ∧ P (x)) The EXPLANATION: For some x, x is FRIEND and funny.

Discussion

30.	The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.(a) ∃x(C(x) ∧ F (x))(b) ∀x(C(x) ∧ F (x))(c) ∃x(C(x) → F (x))(d) ∀x(C(x) → F (x))This question was posed to me during a job interview.Question is taken from Predicate Logic Quantifiers in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct answer is (d) ∀x(C(x) → F (x)) To EXPLAIN: For every person x, if COMEDIAN then x is FUNNY.

Discussion

31.	Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?(a) True(b) FalseThis question was addressed to me by my school principal while I was bunking the class.The doubt is from Predicate Logic Quantifiers in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer»

Discussion

32.	Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?(a) True(b) FalseI got this question during an online interview.This interesting question is from Predicate Logic Quantifiers in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT choice is (b) False Explanation: Because P(x) is false for EVERY REAL NUMBER x, the existential quantification of Q(x), which is ∃xP(x), is false.

Discussion

33.	Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.(a) True(b) FalseI have been asked this question in an interview.Enquiry is from Predicate Logic Quantifiers topic in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer» RIGHT OPTION is (a) True The best EXPLANATION: There are no ELEMENTS in the DOMAIN for which the statement is false.

Discussion

34.	Let Q(x) be the statement “x < 5.” What is the truth value of the quantification ∀xQ(x), having domains as real numbers.(a) True(b) FalseThe question was posed to me in an interview for job.The question is from Predicate Logic Quantifiers topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct option is (b) False To ELABORATE: Q(x) is not true for EVERY REAL NUMBER x, because, for INSTANCE, Q(6) is false. That is, x = 6 is a counterexample for the statement ∀xQ(x). This is false.

Discussion

35.	Let P (x) denote the statement “x >7.” Which of these have truth value true?(a) P (0)(b) P (4)(c) P (6)(d) P (9)This question was addressed to me during an online interview.I would like to ask this question from Predicate Logic Quantifiers in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct answer is (d) P (9) For EXPLANATION I WOULD say: Put x=9, 9>7 which is TRUE.

Discussion

36.	¬ (p ↔ q) is logically equivalent to ________(a) p ↔ ¬q(b) ¬p ↔ q(c) ¬p ↔ ¬q(d) ¬q ↔ ¬pI had been asked this question by my college professor while I was bunking the class.This interesting question is from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT OPTION is (a) p ↔ ¬Q To elaborate: (¬ (p ↔ q)) ↔ (p ↔ ¬q) is tautology.

Discussion

37.	(p → q) ∧ (p → r) is logically equivalent to ________(a) p → (q ∧ r)(b) p → (q ∨ r)(c) p ∧ (q ∨ r)(d) p ∨ (q ∧ r)This question was posed to me in exam.The question is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct choice is (a) p → (Q ∧ R) The best I can explain: ((p → q) ∧ (p → r)) ↔ (p → (q ∧ r)) is TAUTOLOGY.

Discussion

38.	Which of the following statement is correct?(a) p ∨ q ≡ q ∨ p(b) ¬(p ∧ q) ≡ ¬p ∨ ¬q(c) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)(d) All of mentionedThe question was asked at a job interview.My doubt is from Logics in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT answer is (d) All of mentioned Best EXPLANATION: Verify USING TRUTH table, all are correct.

Discussion

39.	(p → r) ∨ (q → r) is logically equivalent to ________(a) (p ∧ q) ∨ r(b) (p ∨ q) → r(c) (p ∧ q) → r(d) (p → q) → rThe question was posed to me during an internship interview.The origin of the question is Logics topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct answer is (C) (p ∧ Q) → r For EXPLANATION: ((p → r) ∨ (q → r)) ↔ ((p ∧ q) → r) is tautology.

Discussion

40.	p ↔ q is logically equivalent to ________(a) (p → q) → (q → p)(b) (p → q) ∨ (q → p)(c) (p → q) ∧ (q → p)(d) (p ∧ q) → (q ∧ p)This question was posed to me in an online quiz.The doubt is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct CHOICE is (c) (p → q) ∧ (q → p) The EXPLANATION: (p ↔ q) ↔ ((p → q) ∧ (q → p)) is TAUTOLOGY.

Discussion

41.	p ∧ q is logically equivalent to ________(a) ¬ (p → ¬q)(b) (p → ¬q)(c) (¬p → ¬q)(d) (¬p → q)I had been asked this question in final exam.I'd like to ask this question from Logics in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT choice is (a) ¬ (p → ¬Q) To explain I would SAY: (p ∧ q) ↔ (¬(p → ¬q)) is TAUTOLOGY.

Discussion

42.	p ∨ q is logically equivalent to ________(a) ¬q → ¬p(b) q → p(c) ¬p → ¬q(d) ¬p → qI got this question during a job interview.My doubt stems from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct ANSWER is (d) ¬P → q Best explanation: (p ∨ q) ↔ (¬p → q) is TAUTOLOGY.

Discussion

43.	p → q is logically equivalent to ________(a) ¬p ∨ ¬q(b) p ∨ ¬q(c) ¬p ∨ q(d) ¬p ∧ qI got this question by my college director while I was bunking the class.My question is from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT option is (C) ¬p ∨ q The explanation is: (p → q) ↔ (¬p ∨ q) is TAUTOLOGY.

Discussion

44.	The compound propositions p and q are called logically equivalent if ________ is a tautology.(a) p ↔ q(b) p → q(c) ¬ (p ∨ q)(d) ¬p ∨ ¬qI got this question in a job interview.The doubt is from Logics in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer»

Discussion

45.	What are the inverse of the conditional statement “If you make your notes, it will be a convenient in exams.”(a) “If you make notes, then it will be a convenient in exams.”(b) “If you do not make notes, then it will not be a convenient in exams.”(c) “If it will not be a convenient in exams, then you did not make your notes.”(d) “If it will be a convenient in exams, then you make your notesThis question was posed to me during an internship interview.My question is taken from Logics in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The CORRECT ANSWER is (b) “If you do not MAKE notes, then it will not be a convenient in EXAMS.” The best explanation: If p then q has inverse ¬p → ¬q.

Discussion

46.	What are the contrapositive of the conditional statement “Medha will find a decent job when she labour hard.”?(a) “If Medha labour hard, then she will find a decent job.”(b) “If Medha will not find a decent job, then she not labour hard.”(c) “If Medha will find a decent job, then she labour hard.”(d) “If Medha not labour hard, then she will not find a decent job.”I have been asked this question in an interview for job.I would like to ask this question from Logics topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer»

Discussion

47.	What are the converse of the conditional statement “When Raj stay up late, it is necessary that Raj sleep until noon.”(a) “If Raj stay up late, then Raj sleep until noon.”(b) “If Raj does not stay up late, then Raj does not sleep until noon.”(c) “If Raj does not sleep until noon, then Raj does not stay up late.”(d) “If Raj sleep until noon, then Raj stay up late.”I had been asked this question during an interview.The origin of the question is Logics topic in portion The Foundation: Logics and Proofs of Discrete Mathematics
Answer» CORRECT answer is (d) “If RAJ sleep until NOON, then Raj stay up late.” Easiest explanation: Necessary condition for P is q has converse q → p.

Discussion

48.	What are the inverse of the conditional statement “ A positive integer is a composite only if it hasdivisors other than 1 and itself.”(a) “A positive integer is a composite if it has divisors other than 1 and itself.”(b) “If a positive integer has no divisors other than 1 and itself, then it is not composite.”(c) “If a positive integer is not composite, then it has no divisors other than 1 and itself.”(d) None of the mentionedThe question was posed to me in an interview.My enquiry is from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics
Answer» The correct choice is (C) “If a positive INTEGER is not composite, then it has no divisors other than 1 and itself.” For explanation I would say: P only if Q has inverse ¬p → ¬q.

Discussion

49.	What are the contrapositive of the conditional statement “I come to class whenever there is going to be a test.”(a) “If I come to class, then there will be a test.”(b) “If I do not come to class, then there will not be a test.”(c) “If there is not going to be a test, then I don’t come to class.”(d) “If there is going to be a test, then I don’t come to class.”The question was posed to me in class test.My doubt stems from Logics topic in section The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct answer is (b) “If I do not come to class, then there will not be a TEST.” To elaborate: Q whenever p, has CONTRAPOSITIVE ¬q → ¬p.

Discussion

50.	What is the converse of the conditional statement “If it ices today, I will play ice hockey tomorrow.”(a) “I will play ice hockey tomorrow only if it ices today.”(b) “If I do not play ice hockey tomorrow, then it will not have iced today.”(c) “If it does not ice today, then I will not play ice hockey tomorrow.”(d) “I will not play ice hockey tomorrow only if it ices today.”This question was posed to me in an online quiz.The origin of the question is Logics in division The Foundation: Logics and Proofs of Discrete Mathematics
Answer» Correct ANSWER is (a) “I will PLAY ice hockey tomorrow only if it ices today.” Best explanation: If P, then q has CONVERSE q → p.

Discussion

Explore topic-wise InterviewSolutions in .

A theorem used to prove other theorems is known as _______________(a) Lemma(b) Corollary(c) Conjecture(d) None of the mentionedI have been asked this question in an online quiz.This question is from Types of Proofs in chapter The Foundation: Logics and Proofs of Discrete Mathematics

The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?(a) p ∨ r(b) p ∨ s(c) p ∨ q(d) q ∨ rThe question was asked during an online interview.I would like to ask this question from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics

Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers.(a) True(b) FalseThe question was posed to me at a job interview.My doubt stems from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics

Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers.(a) True(b) FalseThis question was addressed to me in an interview.My doubt is from Predicate Logic Quantifiers topic in portion The Foundation: Logics and Proofs of Discrete Mathematics

Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A).(a) True(b) FalseI got this question in unit test.I want to ask this question from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics

Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.(a) True(b) FalseI have been asked this question in an interview.Enquiry is from Predicate Logic Quantifiers topic in section The Foundation: Logics and Proofs of Discrete Mathematics

¬ (p ↔ q) is logically equivalent to ________(a) p ↔ ¬q(b) ¬p ↔ q(c) ¬p ↔ ¬q(d) ¬q ↔ ¬pI had been asked this question by my college professor while I was bunking the class.This interesting question is from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics

(p → q) ∧ (p → r) is logically equivalent to ________(a) p → (q ∧ r)(b) p → (q ∨ r)(c) p ∧ (q ∨ r)(d) p ∨ (q ∧ r)This question was posed to me in exam.The question is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics

Which of the following statement is correct?(a) p ∨ q ≡ q ∨ p(b) ¬(p ∧ q) ≡ ¬p ∨ ¬q(c) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)(d) All of mentionedThe question was asked at a job interview.My doubt is from Logics in section The Foundation: Logics and Proofs of Discrete Mathematics

p ↔ q is logically equivalent to ________(a) (p → q) → (q → p)(b) (p → q) ∨ (q → p)(c) (p → q) ∧ (q → p)(d) (p ∧ q) → (q ∧ p)This question was posed to me in an online quiz.The doubt is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics

p ∧ q is logically equivalent to ________(a) ¬ (p → ¬q)(b) (p → ¬q)(c) (¬p → ¬q)(d) (¬p → q)I had been asked this question in final exam.I'd like to ask this question from Logics in portion The Foundation: Logics and Proofs of Discrete Mathematics

p ∨ q is logically equivalent to ________(a) ¬q → ¬p(b) q → p(c) ¬p → ¬q(d) ¬p → qI got this question during a job interview.My doubt stems from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics

p → q is logically equivalent to ________(a) ¬p ∨ ¬q(b) p ∨ ¬q(c) ¬p ∨ q(d) ¬p ∧ qI got this question by my college director while I was bunking the class.My question is from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics

The compound propositions p and q are called logically equivalent if ________ is a tautology.(a) p ↔ q(b) p → q(c) ¬ (p ∨ q)(d) ¬p ∨ ¬qI got this question in a job interview.The doubt is from Logics in portion The Foundation: Logics and Proofs of Discrete Mathematics