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201.

The relation between sets A, B, C as shown by venn diagram is __________(a) A is subset of B and B is subset of C(b) C is nota subset of A and A is subset of B(c) C is subset of B and B is subset of A(d) None of the mentionedI had been asked this question in quiz.My question is taken from Sets in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» RIGHT choice is (c) C is subset of B and B is subset of A

The BEST explanation: As SET C is totally INSIDE set B, set B is totally inside set A.
202.

If n(A)=10, n(B)=30,n(C)=50 and if set A, B, C are pairwise disjoint then which of the following is correct?(a) n(A U B)=0(b) n(B U C)=0(c) n(A U B U C)=90(d) All of the mentionedThis question was addressed to me during an interview.Query is from Sets topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct OPTION is (d) All of the mentioned

To ELABORATE: All the STATEMENTS are TRUE based on definition.

203.

The shaded area of figure is best described by?(a) A‘ (Complement of A)(b) B – (A ∩ B) – (C ∩ B)(c) A ∩ C ∩ B(d) B’ (Complement of B)I got this question in a national level competition.The origin of the question is Sets in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» CORRECT CHOICE is (b) B – (A ∩ B) – (C ∩ B)

Easy EXPLANATION: The region is DIFFERENCE B with A and C.
204.

If n(A)=20 and n(B)=30 and n(A U B) = 40 then n(A ∩ B) is?(a) 20(b) 30(c) 40(d) 10I got this question in a national level competition.My question is taken from Sets topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct CHOICE is (d) 10

Best explanation: N(A U B) = n(A) + n(B) – n(A ∩ B).

205.

The shaded area of figure is best described by?(a) A ∩ B(b) A U B(c) A(d) BThe question was asked by my college professor while I was bunking the class.My question is from Sets in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» CORRECT choice is (a) A ∩ B

The EXPLANATION: The REGION is A intersection B.
206.

The shaded area of figure is best described by?(a) A‘ (Complement of A)(b) A U B -B(c) A ∩ B(d) BThis question was posed to me by my school principal while I was bunking the class.This is a very interesting question from Sets in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct CHOICE is (B) A U B -B

The explanation is: The region is COMPLEMENT of B.

207.

Which sets are not empty?(a) {x: x is a even prime greater than 3}(b) {x : x is a multiple of 2 and is odd}(c) {x: x is an even number and x+3 is even}(d) { x: x is a prime number less than 5 and is odd}This question was addressed to me in my homework.Origin of the question is Set Operations topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» CORRECT ANSWER is (d) { x: x is a prime number less than 5 and is odd}

The best explanation: Because the SET is {3}.
208.

Let A be {1, 2, 3, 4}, U be set of all natural numbers, then U-A’(complement of A) is given by set.(a) {1, 2, 3, 4, 5, 6, ….}(b) {5, 6, 7, 8, 9, ……}(c) {1, 2, 3, 4}(d) All of the mentionedThis question was posed to me by my college professor while I was bunking the class.This interesting question is from Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct OPTION is (c) {1, 2, 3, 4}

To explain I would say: U – A’ ≡ A.

209.

Two sets A and B contains a and b elements respectively. If power set of A contains 16 more elements than that ofB, value of ‘b’ and ‘a’ are _______(a) 4, 5(b) 6, 7(c) 2, 3(d) None of the mentionedI have been asked this question in homework.Origin of the question is Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»
210.

If A is {{Φ}, {Φ, {Φ}}}, then the power set of A has how many element?(a) 2(b) 4(c) 6(d) 8This question was posed to me in an interview for internship.This intriguing question comes from Set Operations topic in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Right OPTION is (b) 4

The best EXPLANATION: The set A has GOT 2 elements so n(P(A))=4.

211.

If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B are ____________(a) 4, 8(b) 8, 12(c) 4, 12(d) None of the mentionedThe question was posed to me in an online interview.This key question is from Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» RIGHT answer is (b) 8, 12

The best I can explain: MINIMUM would be when 4 elements are same as in 8, maximum would be when all are DISTINCT.
212.

Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true?(a) A ≡ B U C(b) B is a singleton set.(c) A ≡ C U {2}(d) All of the mentionedI have been asked this question in quiz.My question is taken from Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct ANSWER is (d) All of the mentioned

Easiest explanation: 2 is the only even PRIME NUMBER.

213.

Let the set A is {1, 2, 3}and B is {2, 3, 4}. Then the setA – B is?(a) {1, -4}(b) {1, 2, 3}(c) {1}(d) {2, 3}The question was posed to me during an internship interview.The origin of the question is Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The CORRECT CHOICE is (c) {1}

BEST explanation: In A – B the common elements get cancelled.

214.

In which of the following sets A – B is equal to B – A?(a) A = {1, 2, 3}, B = {2, 3, 4}(b) A = {1, 2, 3}, B = {1, 2, 3, 4}(c) A = {1, 2, 3}, B = {2, 3, 1}(d) A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 4, 5, 1}I have been asked this question in class test.My question is taken from Set Operations in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The CORRECT option is (C) A = {1, 2, 3}, B = {2, 3, 1}

Best explanation: A- B= B-A = EMPTY set.

215.

Let the set A is {1, 2, 3}and B is { 2, 3, 4}. Then number of elements in A ∩ B is?(a) 1(b) 2(c) 3(d) 4This question was addressed to me in semester exam.The above asked question is from Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» RIGHT CHOICE is (B) 2

The best explanation: A ∩ B is {2, 3}.
216.

Let the set A is {1, 2, 3}and B is {2, 3, 4}. Then the number of elements in A U B is?(a) 4(b) 5(c) 6(d) 7The question was posed to me in semester exam.I need to ask this question from Set Operations topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct OPTION is (a) 4

Best explanation: AUB is {1, 2, 3, 4}.

217.

The set difference of the set A with null set is __________(a) A(b) null(c) U(d) BI got this question in an international level competition.I need to ask this question from Set Operations topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Right ANSWER is (a) A

Best EXPLANATION: The set DIFFERENCE of the set A by the null set DENOTED by A – {null} is A.

218.

The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________(a) 1010100000(b) 1010101101(c) 1111111100(d) 1111101010I have been asked this question at a job interview.The doubt is from Set Operations topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Right answer is (d) 1111101010

For explanation I WOULD SAY: The bit string for the union is the BITWISE OR of the bit STRINGS.

219.

Let Ai = {i, i+1, i+2, …..}. Then set {n, n+1, n+2, n+3, …..} is the _________ of the set Ai.(a) Union(b) Intersection(c) Set Difference(d) DisjointI had been asked this question in an interview.Question is taken from Set Operations topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The CORRECT answer is (b) Intersection

To EXPLAIN: By the DEFINITION of the generalized intersection of the SET.

220.

The bit string for the set {2, 4, 6, 8, 10} (with universal set of natural numbers less than or equal to 10) is ____________________(a) 0101010101(b) 1010101010(c) 1010010101(d) 0010010101The question was asked during an interview.The origin of the question is Set Operations topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct choice is (a) 0101010101

For explanation: The bit string for the set has a one bit in second, fourth, sixth, EIGHTH, tenth POSITIONS, and a ZERO ELSEWHERE.

221.

The complement of the set A is _____________(a) A – B(b) U – A(c) A – U(d) B – AI got this question in an international level competition.I'm obligated to ask this question of Set Operations topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct choice is (B) U – A

For EXPLANATION: The COMPLEMENT of the set A is the complement of A with respect to U.

222.

The difference of {1, 2, 3} and {1, 2, 5} is the set ____________(a) {1}(b) {5}(c) {3}(d) {2}This question was posed to me during an interview.I'd like to ask this question from Set Operations in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct choice is (c) {3}

For explanation I would SAY: The DIFFERENCE of the SETS A and B DENOTED by A-B, is the set containing those elements that are in A not in B.

223.

Two sets are called disjoint if there _____________ is the empty set.(a) Union(b) Difference(c) Intersection(d) ComplementI got this question in homework.This key question is from Set Operations in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Right OPTION is (C) Intersection

Explanation: By the DEFINITION of the DISJOINT set.

224.

The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________(a) {1, 2}(b) {5, 6}(c) {2, 5}(d) {1, 6}I got this question at a job interview.Query is from Set Operations in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct answer is (a) {1, 2}

To EXPLAIN: The INTERSECTION of the SETS A and B, is the set containing those elements that are in both A and B.

225.

Which of the following two sets are disjoint?(a) {1, 3, 5} and {1, 3, 6}(b) {1, 2, 3} and {1, 2, 3}(c) {1, 3, 5} and {2, 3, 4}(d) {1, 3, 5} and {2, 4, 6}The question was posed to me in an interview for internship.This intriguing question comes from Set Operations in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» CORRECT answer is (d) {1, 3, 5} and {2, 4, 6}

To elaborate: TWO sets are disjoint if the intersection of two sets is the empty set.
226.

The members of the set S = {x | x is the square of an integer and x < 100} is ________________(a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}(b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}(c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}(d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}I had been asked this question in a national level competition.This interesting question is from Sets in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Right answer is (b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

To explain: The set S CONSISTS of the SQUARE of an integer less than 10.

227.

The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________(a) {1, 2, 6, 1}(b) {1, 2, 5, 6}(c) {1, 2, 1, 2}(d) {1, 5, 6, 3}I got this question at a job interview.This is a very interesting question from Set Operations in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» CORRECT answer is (b) {1, 2, 5, 6}

To explain: The union of the SETS A and B, is the SET that contains those ELEMENTS that are either in A or in B.
228.

The set of positive integers is _____________(a) Infinite(b) Finite(c) Subset(d) EmptyThe question was posed to me in an interview for internship.This key question is from Sets topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»
229.

Which of the following two sets are equal?(a) A = {1, 2} and B = {1}(b) A = {1, 2} and B = {1, 2, 3}(c) A = {1, 2, 3} and B = {2, 1, 3}(d) A = {1, 2, 4} and B = {1, 2, 3}I had been asked this question by my college director while I was bunking the class.My query is from Sets topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct answer is (c) A = {1, 2, 3} and B = {2, 1, 3}

The explanation is: TWO SET are EQUAL if and only if they have the same ELEMENTS.

230.

What is the Cardinality of the Power set of the set {0, 1, 2}?(a) 8(b) 6(c) 7(d) 9The question was posed to me by my college professor while I was bunking the class.I would like to ask this question from Sets in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»
231.

What is the cardinality of the set of odd positive integers less than 10?(a) 10(b) 5(c) 3(d) 20This question was addressed to me during an online interview.My question is taken from Sets topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct option is (b) 5

For explanation: SET S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.

232.

What is the Cartesian product of A = {1, 2} and B = {a, b}?(a) {(1, a), (1, b), (2, a), (b, b)}(b) {(1, 1), (2, 2), (a, a), (b, b)}(c) {(1, a), (2, a), (1, b), (2, b)}(d) {(1, 1), (a, a), (2, a), (1, b)}I got this question in an internship interview.Enquiry is from Sets in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct choice is (C) {(1, a), (2, a), (1, b), (2, b)}

The best I can EXPLAIN: A subset R of the Cartesian product A x B is a relation from the SET A to the set B.

233.

The Cartesian Product B x A is equal to the Cartesian product A x B.(a) True(b) FalseThe question was posed to me by my school teacher while I was bunking the class.My question is based upon Sets in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct answer is (b) False

Best EXPLANATION: LET A = {1, 2} and B = {a, b}. The CARTESIAN product A x B = {(1, a), (1, b), (2, a), (2, b)} and the Cartesian product B x A = {(a, 1), (a, 2), (b, 1), (b, 2)}. This is not EQUAL to A x B.

234.

Power set of empty set has exactly _________ subset.(a) One(b) Two(c) Zero(d) ThreeI have been asked this question during an interview.My question is from Sets topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct ANSWER is (a) One

The best EXPLANATION: Power set of NULL set has exactly one subset which is empty set.

235.

The set O of odd positive integers less than 10 can be expressed by _____________(a) {1, 2, 3}(b) {1, 3, 5, 7, 9}(c) {1, 2, 5, 9}(d) {1, 5, 7, 9, 11}This question was posed to me by my college director while I was bunking the class.Asked question is from Sets in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct OPTION is (B) {1, 3, 5, 7, 9}

EXPLANATION: Odd NUMBERS less than 10 is {1, 3, 5, 7, 9}.

236.

A __________ is an ordered collection of objects.(a) Relation(b) Function(c) Set(d) PropositionI had been asked this question during a job interview.The doubt is from Sets topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The CORRECT ANSWER is (c) SET

To ELABORATE: By the DEFINITION of set.

237.

Convert set {x: x is a positive prime number which divides 72} in roster form.(a) {2, 3, 5}(b) {2, 3, 6}(c) {2, 3}(d) {∅}I had been asked this question during an online exam.Question is taken from Types of Set in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct option is (C) {2, 3}

To explain I would SAY: 2 and 3 are thedivisors of 72 which are PRIME.

238.

{x: x ∈ N and x is prime} then it is ________(a) Infinite set(b) Finite set(c) Empty set(d) Not a setI have been asked this question in final exam.Enquiry is from Types of Set topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» RIGHT answer is (a) INFINITE set

Explanation: There is no EXTREME PRIME, number of primes is infinite.
239.

Subset of the set A= { } is?(a) A(b) {}(c) ∅(d) All of the mentionedI have been asked this question in a national level competition.I need to ask this question from Types of Set in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct choice is (d) All of the mentioned

The BEST explanation: EVERY SET is SUBSET of itself and Empty set is subset of each set.

240.

A = {∅,{∅},2,{2,∅},3}, which of the following is true?(a) {{∅,{∅}} ∈ A(b) {2} ∈ A(c) ∅ ⊂ A(d) 3 ⊂ AThe question was posed to me in unit test.This is a very interesting question from Types of Set in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Correct option is (C) ∅ ⊂ A

Explanation: Empty set is a SUBSET of EVERY set.

241.

Which of the following is subset of set {1, 2, 3, 4}?(a) {1, 2}(b) {1, 2, 3}(c) {1}(d) All of the mentionedI had been asked this question during a job interview.Origin of the question is Types of Set topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

Right OPTION is (d) All of the mentioned

For explanation: There are total 16 SUBSETS.

242.

Express {x: x= n/ (n+1), n is a natural number less than 7} in roster form.(a) {^1⁄2, ^2⁄3, ^4⁄5, ^6⁄7}(b) {^1⁄2, ^2⁄3, ^3⁄4, ^4⁄5, ^5⁄6, ^6⁄7, ^7⁄8}(c) {^1⁄2, ^2⁄3, ^3⁄4, ^4⁄5, ^5⁄6, ^6⁄7}(d) Infinite setI had been asked this question by my school teacher while I was bunking the class.This interesting question is from Types of Set in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct choice is (c) {^1⁄2, ^2⁄3, ^3⁄4, ^4⁄5, ^5⁄6, ^6⁄7}

To explain: N/(n+1) = 1/(1+1) = ^1⁄2 and n>7.

243.

Number of power set of {a, b}, where a and b are distinct elements.(a) 3(b) 4(c) 2(d) 5I have been asked this question during an online interview.I'd like to ask this question from Types of Set topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» CORRECT CHOICE is (B) 4

Explanation: POWER SET of {a, b} = {∅, {a, b}, {a}, {b}}.
244.

Write set {1, 5, 15, 25,…} in set-builder form.(a) {x: either x=1 or x=5n, where n is a real number}(b) {x: either x=1 or x=5n, where n is a integer}(c) {x: either x=1 or x=5n, where n is an odd natural number}(d) {x: x=5n, where n is a natural number}This question was posed to me in an online quiz.My query is from Types of Set topic in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct option is (c) {x: either x=1 or x=5n, where n is an odd NATURAL NUMBER}

For EXPLANATION: Set should INCLUDE 1 or an odd multiple of 5.

245.

{x: x is a real number between 1 and 2} is an ________(a) Infinite set(b) Finite set(c) Empty set(d) None of the mentionedI got this question in an online interview.This interesting question is from Types of Set in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct answer is (a) INFINITE set

Easiest explanation: It is an infinite set as there are INFINITELY MANY real number between any two different real numbers.

246.

{x: x is an integer neither positive nor negative} is ________(a) Empty set(b) Non-empty set(c) Finite set(d) Non- empty and Finite setThe question was posed to me in class test.The query is from Types of Set in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer» RIGHT option is (d) NON- empty and Finite SET

Explanation: Set = {0} non-empty and finite set.