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.

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 5 of 12

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Q41.

Which of the following statements is the negation of the statements “4 is odd or -9 is positive”?

4 is even or -9 is not negative

4 is odd or -9 is not negative

4 is even and -9 is negative

4 is odd and -9 is not negative

Discuss

Answer: (c).4 is even and -9 is negative

Q42.

Which of the following represents: ~A (negation of A) if A stands for “I like badminton but hate maths”?

I hate badminton and maths

I do not like badminton or maths

I dislike badminton but love maths

I hate badminton or like maths

Discuss

Answer: (d).I hate badminton or like maths

Q43.

The compound statement A v ~(A ∧ B).

True

False

May be True or False

Can't say

Discuss

Answer: (a).True

Q44.

Which of the following is De-Morgan’s law?

P ∧ (Q v R) Ξ (P ∧ Q) v (P ∧ R)

~(P ∧ R) Ξ ~P v ~R, ~(P v R) Ξ ~P ∧ ~R

P v ~P Ξ True, P ∧ ~P Ξ False

None of the mentioned

Discuss

Answer: (b).~(P ∧ R) Ξ ~P v ~R, ~(P v R) Ξ ~P ∧ ~R

Q45.

What is the dual of (A ∧ B) v (C ∧ D)?

(A V B) v (C v D)

(A V B) ^ (C v D)

(A V B) v (C ∧ D)

(A ∧ B) v (C v D)

Discuss

Answer: (b).(A V B) ^ (C v D)

Q46.

~ A v ~ B is logically equivalent to?

~ A → ~ B

~ A ∧ ~ B

A → ~B

B V A

Discuss

Answer: (c).A → ~B

Q47.

Negation of statement (A ∧ B) → (B ∧ C) is _____________

(A ∧ B) →(~B ∧ ~C)

~(A ∧ B) v ( B v C)

~(A →B) →(~B ∧ C)

None of the mentioned

Discuss

Answer: (a).(A ∧ B) →(~B ∧ ~C)

Q48.

Which of the following satisfies commutative law?

∧

↔

All of the mentioned

Discuss

Answer: (d).All of the mentioned

Q49.

If the truth value of A v B is true, then truth value of ~A ∧ B can be ___________

True if A is false

False if A is false

False if B is true and A is false

None of the mentioned

Discuss

Answer: (a).True if A is false

Q50.

If P is always against the testimony of Q, then the compound statement P→(P v ~Q) is a __________

Tautology

Contradiction

Contingency

None of the mentioned

Discuss

Answer: (a).Tautology

Page 5 of 12

Welcome to the Logics and Proofs MCQs Page

Logics and Proofs MCQs | Page 5 of 12

Explore more Topics under Discrete Mathematics

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

Group Theory

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