64 + Interview Questions in MATHEMATICAL-LOGIC IN GENERAL AWARENESS Page 1 InterviewSolution

1.	The only statement among the following i.e. a tautology isA. `Bto[A^^(AtoB)]`B. `A^^(AvvB)`C. `Avv(A^^B)`D. `[A^^(AtoB)]toB`
Answer» Correct Answer - D

Discussion

2.	If p: Sam is fat,q : Sam is happy,indicate the symbolic form of the following verbal statements If sam is fat, then he is happy.A. `pharrq`B. `pharr~q`C. `prarrq`D. `~prarrq`
Answer» Correct Answer - C

Discussion

3.	If p: Sam is fat,q : Sam is happy,indicate the symbolic form of the following verbal statements Sam is thin but happy.A. `~pvvq`B. `pvv~q`C. `p^^~q`D. `~p^^q`
Answer» Correct Answer - D

Discussion

4.	If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements If price does not increses, then demand does not fall.A. `~qto~p`B. `qto"p"`C. `pvv~q`D. `~pto~q`
Answer» Correct Answer - D

Discussion

5.	If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements If demand does not fall, then price does not incresesA. `~q^^~q`B. `~qto~p`C. `qto p`D. `ptoq`
Answer» Correct Answer - B

Discussion

6.	If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements Price increase if, and only if, demand falls.A. `pharrq`B. `qtoq`C. `qtoq`D. `q^^q`
Answer» Correct Answer - A

Discussion

7.	The negation of the statement : 'If a person is social, then he is happy.' isA. If a person is not social then he is not haapy.B. A person is social but not happy.C. If a person is not social then he is happy.D. If a person is happy then he is social.
Answer» Correct Answer - A person is social but not happy.

Discussion

8.	The converse of the contrapriate of ptoq is.A. `~ptoq`B. `qto""p`C. `pto~q`D. `~qto~p`
Answer» Correct Answer - `pto~q`

Discussion

9.	If p,q,r are single proposition with truth values T, F, F, then the truth value of `(p ^^ ~ q) to (~p vv r)` isA. TB. FC. Cannot findD. Both T and F
Answer» Correct Answer - B

Discussion

10.	If statements `(p^^q)`" and `[(p^^q)harrq]` are both false, then truth-values of p and q are respectivelyA. T,FB. F,TC. F,FD. T,T
Answer» Correct Answer - B

Discussion

11.	The statement `p to(q to p)` is equivalent toA. `pto(harrq)`B. `pto(ptoq)`C. `pto(pvvq)`D. `pto(p^^q)`
Answer» Correct Answer - C

Discussion

12.	If p : If the dozen is thirteen, then this sentence will contain thirteen words, thenA. truth-value of p is TB. truth-value of p is FC. p is both true and falseD. p is neither true nor false
Answer» Correct Answer - D

Discussion

13.	If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `[p^^(q^^r)]vv~[(pvvq)^^(~rvvs)]`A. TB. FC. both T and FD. 10
Answer» Correct Answer - B

Discussion

14.	`(p ^^ q) vv ~ p` is equivalent toA. `~p^^q`B. `~pvvq`C. `p^^q`D. `pvvq`
Answer» Correct Answer - C

Discussion

15.	The simplified form of `(p^^q)vv(p^^~q)` isA. pB. qC. `p^^q`D. `pvvq`
Answer» Correct Answer - A

Discussion

16.	The dual of the statement `(p^^q)vv~q=pvv~q` isA. `(pvv)~q=pvv~q`B. `(p^^q)^^~q=pvv~q`C. `(pvvq)^^~q=p^^~q`D. `(q^^p)vv~p=qvv~p`
Answer» Correct Answer - C

Discussion

17.	The negation of `~p^^(qtor)` isA. `p^^(~q^^~r)`B. `~p^^(~q^^~r)`C. `p^^(~q^^~r)`D. `~p^^(qtor)`
Answer» Correct Answer - `~pvv(q^^~r)`

Discussion

18.	The negation of the statement `(~pvv~q)vv(p^^~q)` isA. `ptoq`B. `pharrq`C. `(p^^~q)^^(pvv~q)`D. `qtop`
Answer» Correct Answer - B

Discussion

19.	If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `[(~p^^q)^^~r]vv[(qtor)to(~svvr)]`A. TB. FC. both T and FD. 0
Answer» Correct Answer - A

Discussion

20.	Which of the following is the conditional `p to q`?A. `pto~q`B. `~pvvq`C. `~pto~q`D. `pvv~q`
Answer» Correct Answer - B

Discussion

21.	The simplified form of the circuit : isA. B. C. D.
Answer» Correct Answer - C

Discussion

22.	Negation of `'AuuB=B` is the sufficient condition for `AsubeB'` isA. `AuuB=BandAcancelsubB`B. `AuuBneB" but "AsubeB`C. If `AcancelsubeB," then "AuuBneB`D. `AnnB=BandAsubeB`
Answer» Correct Answer - `AuuB=BandAcancelsubeB`

Discussion

23.	If `p^^q=F,ptoq=F` then the truth values of p and q areA. T, TB. T, FC. F, TD. F, F
Answer» Correct Answer - `T.F`

Discussion

24.	If `A={2,3,4,5,6}`, Then which of the following is not true ?A. `EEx""inA,` such that `x+3=8`B. `EEx""inA,` such that `x+2lt5`C. `AAx""inA`, such that `x+2lt9`D. `AAx""inA,` such that `x+6ge9`
Answer» Correct Answer - `AAx""inA` such that `x+6ge9`

Discussion

25.	Inverse of statement pattern `(pvvq)to(p^^q)` isA. `(p^^q)to(pvvq)`B. `~(pvvq)to(p^^q)`C. `(~pvv~q)to(~p^^~q)`D. `(~p^^~q)to(~pvv~q)`
Answer» Correct Answer - `(~p^^~q)to(~p vv~q)`

Discussion

26.	The negation of inverse of `~ptoq` isA. `~qto""p`B. `p^^~q`C. `~p^^q`D. `p^^q`
Answer» Correct Answer - `p^^q`

Discussion

27.	If `(p^^~r) to (~p vvq)` is false, then truth values of p,q and r are respectively.A. F,F,TB. T,F,FC. F,T,TD. T,F,T
Answer» Correct Answer - B

Discussion

28.	Which of the following statements is contingency?A. `[ptoq]^^(qtor)]to(ptor)`B. `pto(pvvq)`C. `[pto (qtor)]harr[(p^^q)tor]`D. `(p^^q)vvr`
Answer» Correct Answer - D

Discussion

29.	The statement `~(pharr ~q)` isA. equivalent to `ptoq`B. equivalent to `~ptoq`C. a tautoloyD. a faallacy
Answer» Correct Answer - A

Discussion

30.	The negation of the statement "If I becomes a teacher, then I will open a school", isA. I will become a teacher and I will not open a schoolB. Either I will not become a teacher or I will not open a schoolC. Neither I will become a teacher a nor I will open a schoolD. I will not become a teacher a teacher nor I will open a school
Answer» Correct Answer - A

Discussion

31.	If statements t and f represent a tautology and a contradiction (fallacy) respectively, then `pvvf equiv`A. tB. fC. pD. 2
Answer» Correct Answer - C

Discussion

32.	Ifp : Square of any real number is positive, q:5+4=11 and r: Square of any odd number is even, which of the following has truth-value T?A. PB. qC. rD. `~pwedge~qwedge~r`
Answer» Correct Answer - D

Discussion

33.	Ifp: `sin2theta=2sinthetacostheta" where "theta` is mango,q: `sin2theta=2sinthetacostheta`for all `theta`,r:`sin2theta=2sinthetacos theta`for all real values of `theta,`which of them is not a statement?A. pB. qC. rD. p or r
Answer» Correct Answer - B

Discussion

34.	The equivalent of `(Pto~p)vv(~pto"p")` is :A. FB. `(Pto~p)^^(~pto"p")`C. `pvvT`D. `p^^~p`
Answer» Correct Answer - C

Discussion

35.	The negation of `~pto(qvvr)` isA. `p^^(~q^^~r)`B. `~p^^(~q^^~r)`C. `p^^(~qvv~r)`D. `~pvv(~q^^~r)`.
Answer» Correct Answer - `~p^^(~q^^~r)`

Discussion

36.	If p: Mumbai is the capital of India, `q:x^(2)-5x-6=0` when x=2, r : 829 is divisible by 9, which fo them has truth-valueT?A. pB. ~qC. rD. p or r
Answer» Correct Answer - B

Discussion

37.	If P : Every natural number is whole number, q : Equation `x^(2)-3x+2=0` has two real roots, r :36 is a prime number, which of them has truth-value F?A. pB. qC. rD. p or r
Answer» Correct Answer - C

Discussion

38.	If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `~qvv(~ptor)`A. TB. FC. both T and FD. 0
Answer» Correct Answer - A

Discussion

39.	If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements [If] Prcie increases, then demand falls.A. `qtoq`B. `ptoq`C. `~qvvq`D. `q^^q`
Answer» Correct Answer - B

Discussion

40.	If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `~q^^(rtoq)`A. TB. FC. both T and FD. 1
Answer» Correct Answer - B

Discussion

41.	If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in It is not true that Rohit is short or not handsome.A. `~(~p^^~q)`B. `~(~p^^~q)`C. `~pvv~q`D. `p^^q`
Answer» Correct Answer - D

Discussion

42.	If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in Rohit is tall and handsome.A. `pveeq`B. `p^^q`C. `ptoq`D. `pharrq`
Answer» Correct Answer - B

Discussion

43.	If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in It is false that Rohit is short or handsome.A. `~(p^^q)`B. `pvv~q`C. `p^^~q`D. `~(p^^q)`
Answer» Correct Answer - C

Discussion

44.	If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in Rohit is tall or not handsome.A. `~pvv~q`B. `~pvvq`C. `pvv~q`D. `(pvvq)`
Answer» Correct Answer - C

Discussion

45.	If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in Rohit is tall, or he is short and handsome.A. `pvv(~p^^q)`B. `p^^(~p^^q)`C. `pvv(p^^~q)`D. `pvv~(p^^q)`
Answer» Correct Answer - A

Discussion

46.	If p : It is cold, q : It is raining. Indiacate the verbal form of the following symbolic statements `qvv~p`A. It is raining and it is not cold.B. It is rainingj or it is not cold.C. It is raining but cold.D. None of these
Answer» Correct Answer - B

Discussion

47.	If p : It is cold, q : It is raining indiacate the verbal form of the following symbolic statements `~p^^~q`A. It is neither cold nor raining.B. It is not either cold or hot.C. It has stopped raining yet it is cold.D. It is not cold or raining.
Answer» Correct Answer - A

Discussion

48.	If p is any statement, then `(p^^~)` is aA. contingencyB. contradictionC. tautologyD. paradox
Answer» Correct Answer - C

Discussion

49.	If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `(~rharrp)to~q`A. TB. FC. both T and FD. 1
Answer» Correct Answer - B

Discussion

50.	If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `~[(p^^r)]vv(~qvvs)`A. TB. FC. both T and FD. 1
Answer» Correct Answer - A::D

Discussion

Explore topic-wise InterviewSolutions in .

The only statement among the following i.e. a tautology isA. `Bto[A^^(AtoB)]`B. `A^^(AvvB)`C. `Avv(A^^B)`D. `[A^^(AtoB)]toB`

If p: Sam is fat,q : Sam is happy,indicate the symbolic form of the following verbal statements If sam is fat, then he is happy.A. `pharrq`B. `pharr~q`C. `prarrq`D. `~prarrq`

If p: Sam is fat,q : Sam is happy,indicate the symbolic form of the following verbal statements Sam is thin but happy.A. `~pvvq`B. `pvv~q`C. `p^^~q`D. `~p^^q`

If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements If price does not increses, then demand does not fall.A. `~qto~p`B. `qto"p"`C. `pvv~q`D. `~pto~q`

If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements If demand does not fall, then price does not incresesA. `~q^^~q`B. `~qto~p`C. `qto p`D. `ptoq`

If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements Price increase if, and only if, demand falls.A. `pharrq`B. `qtoq`C. `qtoq`D. `q^^q`

The negation of the statement : 'If a person is social, then he is happy.' isA. If a person is not social then he is not haapy.B. A person is social but not happy.C. If a person is not social then he is happy.D. If a person is happy then he is social.

The converse of the contrapriate of ptoq is.A. `~ptoq`B. `qto""p`C. `pto~q`D. `~qto~p`

If p,q,r are single proposition with truth values T, F, F, then the truth value of `(p ^^ ~ q) to (~p vv r)` isA. TB. FC. Cannot findD. Both T and F

If statements `(p^^q)`" and `[(p^^q)harrq]` are both false, then truth-values of p and q are respectivelyA. T,FB. F,TC. F,FD. T,T

The statement `p to(q to p)` is equivalent toA. `pto(harrq)`B. `pto(ptoq)`C. `pto(pvvq)`D. `pto(p^^q)`

If p : If the dozen is thirteen, then this sentence will contain thirteen words, thenA. truth-value of p is TB. truth-value of p is FC. p is both true and falseD. p is neither true nor false

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `[p^^(q^^r)]vv~[(pvvq)^^(~rvvs)]`A. TB. FC. both T and FD. 10

`(p ^^ q) vv ~ p` is equivalent toA. `~p^^q`B. `~pvvq`C. `p^^q`D. `pvvq`

The simplified form of `(p^^q)vv(p^^~q)` isA. pB. qC. `p^^q`D. `pvvq`

The dual of the statement `(p^^q)vv~q=pvv~q` isA. `(pvv)~q=pvv~q`B. `(p^^q)^^~q=pvv~q`C. `(pvvq)^^~q=p^^~q`D. `(q^^p)vv~p=qvv~p`

The negation of `~p^^(qtor)` isA. `p^^(~q^^~r)`B. `~p^^(~q^^~r)`C. `p^^(~q^^~r)`D. `~p^^(qtor)`

The negation of the statement `(~pvv~q)vv(p^^~q)` isA. `ptoq`B. `pharrq`C. `(p^^~q)^^(pvv~q)`D. `qtop`

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `[(~p^^q)^^~r]vv[(qtor)to(~svvr)]`A. TB. FC. both T and FD. 0

Which of the following is the conditional `p to q`?A. `pto~q`B. `~pvvq`C. `~pto~q`D. `pvv~q`

The simplified form of the circuit : isA. B. C. D.

Negation of `'AuuB=B` is the sufficient condition for `AsubeB'` isA. `AuuB=BandAcancelsubB`B. `AuuBneB" but "AsubeB`C. If `AcancelsubeB," then "AuuBneB`D. `AnnB=BandAsubeB`

If `p^^q=F,ptoq=F` then the truth values of p and q areA. T, TB. T, FC. F, TD. F, F

If `A={2,3,4,5,6}`, Then which of the following is not true ?A. `EEx""inA,` such that `x+3=8`B. `EEx""inA,` such that `x+2lt5`C. `AAx""inA`, such that `x+2lt9`D. `AAx""inA,` such that `x+6ge9`

Inverse of statement pattern `(pvvq)to(p^^q)` isA. `(p^^q)to(pvvq)`B. `~(pvvq)to(p^^q)`C. `(~pvv~q)to(~p^^~q)`D. `(~p^^~q)to(~pvv~q)`

The negation of inverse of `~ptoq` isA. `~qto""p`B. `p^^~q`C. `~p^^q`D. `p^^q`

If `(p^^~r) to (~p vvq)` is false, then truth values of p,q and r are respectively.A. F,F,TB. T,F,FC. F,T,TD. T,F,T

Which of the following statements is contingency?A. `[ptoq]^^(qtor)]to(ptor)`B. `pto(pvvq)`C. `[pto (qtor)]harr[(p^^q)tor]`D. `(p^^q)vvr`

The statement `~(pharr ~q)` isA. equivalent to `ptoq`B. equivalent to `~ptoq`C. a tautoloyD. a faallacy

If statements t and f represent a tautology and a contradiction (fallacy) respectively, then `pvvf equiv`A. tB. fC. pD. 2

Ifp : Square of any real number is positive, q:5+4=11 and r: Square of any odd number is even, which of the following has truth-value T?A. PB. qC. rD. `~pwedge~qwedge~r`

Ifp: `sin2theta=2sinthetacostheta" where "theta` is mango,q: `sin2theta=2sinthetacostheta`for all `theta`,r:`sin2theta=2sinthetacos theta`for all real values of `theta,`which of them is not a statement?A. pB. qC. rD. p or r

The equivalent of `(Pto~p)vv(~pto"p")` is :A. FB. `(Pto~p)^^(~pto"p")`C. `pvvT`D. `p^^~p`

The negation of `~pto(qvvr)` isA. `p^^(~q^^~r)`B. `~p^^(~q^^~r)`C. `p^^(~qvv~r)`D. `~pvv(~q^^~r)`.

If p: Mumbai is the capital of India, `q:x^(2)-5x-6=0` when x=2, r : 829 is divisible by 9, which fo them has truth-valueT?A. pB. ~qC. rD. p or r

If P : Every natural number is whole number, q : Equation `x^(2)-3x+2=0` has two real roots, r :36 is a prime number, which of them has truth-value F?A. pB. qC. rD. p or r

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `~qvv(~ptor)`A. TB. FC. both T and FD. 0

If p : price increase,q : demand falls, indicate the symbolic form of the following verbal statements [If] Prcie increases, then demand falls.A. `qtoq`B. `ptoq`C. `~qvvq`D. `q^^q`

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `~q^^(rtoq)`A. TB. FC. both T and FD. 1

If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in It is not true that Rohit is short or not handsome.A. `~(~p^^~q)`B. `~(~p^^~q)`C. `~pvv~q`D. `p^^q`

If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in Rohit is tall and handsome.A. `pveeq`B. `p^^q`C. `ptoq`D. `pharrq`

If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in It is false that Rohit is short or handsome.A. `~(p^^q)`B. `pvv~q`C. `p^^~q`D. `~(p^^q)`

If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in Rohit is tall or not handsome.A. `~pvv~q`B. `~pvvq`C. `pvv~q`D. `(pvvq)`

If p: Rohit is tall q:Rohit is handsome, indicate the symbolic form of the following statement [ in Rohit is tall, or he is short and handsome.A. `pvv(~p^^q)`B. `p^^(~p^^q)`C. `pvv(p^^~q)`D. `pvv~(p^^q)`

If p : It is cold, q : It is raining. Indiacate the verbal form of the following symbolic statements `qvv~p`A. It is raining and it is not cold.B. It is rainingj or it is not cold.C. It is raining but cold.D. None of these

If p : It is cold, q : It is raining indiacate the verbal form of the following symbolic statements `~p^^~q`A. It is neither cold nor raining.B. It is not either cold or hot.C. It has stopped raining yet it is cold.D. It is not cold or raining.

If p is any statement, then `(p^^~)` is aA. contingencyB. contradictionC. tautologyD. paradox

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `(~rharrp)to~q`A. TB. FC. both T and FD. 1

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement `~[(p^^r)]vv(~qvvs)`A. TB. FC. both T and FD. 1