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Welcome to the Logics and Proofs MCQs Page

Dive deep into the fascinating world of Logics and Proofs with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Logics and Proofs, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Logics and Proofs, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Logics and Proofs. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Logics and Proofs. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Logics and Proofs MCQs | Page 4 of 12

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Q31.
Let P: We give a nice overall squad performance, Q: We will win the match.
Then the symbolic form of “We will win the match if and only if we give a nice overall squad performance.“ is?

a.

P v Q

b.

Q ∧ P

c.

Q<->P

d.

~P v Q

Discuss
Answer: (c).Q<->P
Q32.
Let P, Q, R be true, false true, respectively, which of the following is true?

a.

P∧Q∧R

b.

P∧~Q∧~R

c.

Q->(P∧R)

d.

P->(Q∧R)

Discuss
Answer: (c).Q->(P∧R)
Q33.
“Match will be played only if it is not a humid day.” The negation of this statement is?

a.

Match will be played but it is a humid day

b.

Match will be played or it is a humid day

c.

All of the mentioned statement are correct

d.

None of the mentioned

Discuss
Answer: (a).Match will be played but it is a humid day
Q34.
Consider the following statements.

A: Raju should exercise.
B: Raju is not a decent table tennis player.
C: Raju wants to play good table tennis.

The symbolic form of “Raju is not a decent table tennis player and if he wants to play good table tennis then he should exercise.” is?

a.

A->B->C

b.

B∧(C->A)

c.

C->B∧A

d.

B<->A∧C

Discuss
Answer: (b).B∧(C->A)
Q35.
The statement (~P<->Q)∧~Q is true when?

a.

P: True Q: False

b.

P: True Q: True

c.

P: False Q: True

d.

P: False Q: False

Discuss
Answer: (a).P: True Q: False
Q36.
Let P, Q, R be true, false, false, respectively, which of the following is true?

a.

P∧(Q∧~R)

b.

(P->Q)∧~R

c.

Q<->(P∧R)

d.

P<->(QvR)

Discuss
Answer: (c).Q<->(P∧R)
Q37.
If there are ‘M’ switches in series numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary?

a.

1∧ 2∧ 3 ∧ … ∧M should be on

b.

1∧ 2∧ 3 ∧ … ∧M should be off

c.

1 v 2 v 3 v … v M should be on

d.

None of the mentioned

Discuss
Answer: (a).1∧ 2∧ 3 ∧ … ∧M should be on
Q38.
If there are ‘M’ switches in parallel numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary

a.

1∧ 2∧ 3 ∧ … ∧M should be on

b.

1∧ 2∧ 3 ∧ … ∧M should be off

c.

1 v 2 v 3 v … v M should be on

d.

None of the mentioned

Discuss
Answer: (c).1 v 2 v 3 v … v M should be on
Q39.
If in a for it to be complete it is necessary for switch A to be closed and either of switch B or C to be closed, then which can be true?

a.

Switch A should in parallel with B and C is series to them

b.

Switch A should be in series with a parallel circuit of B and C

c.

All of the mentioned

d.

None of the mentioned

Discuss
Answer: (b).Switch A should be in series with a parallel circuit of B and C
Q40.
Which of the following statements is the negation of the statements “4 is odd or -9 is positive”?

a.

4 is even or -9 is not negative

b.

4 is odd or -9 is not negative

c.

4 is even and -9 is negative

d.

4 is odd and -9 is not negative

Discuss
Answer: (c).4 is even and -9 is negative
Page 4 of 12

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