Engineering Questions with Answers - Multiple Choice Questions

# MCQs on Logics – Tautologies and Contradictions

1 - Question

. A compound proposition that is always ___________ is called a tautology.
a) True
b) False

Explanation: Tautology is always true.

2 - Question

A compound proposition that is always ___________ is called a contradiction.
a) True
b) False

3 - Question

If A is any statement, then which of the following is a tautology?
a) A ∧ F
b) A ∨ F
c) A ∨ ¬A
d) A ∧ T

Explanation: A ∨ ¬A is always true.

4 - Question

If A is any statement, then which of the following is not a contradiction?
a) A ∧ ¬A
b) A ∨ F
c) A ∧ F
d) None of mentioned

Explanation: A ∨ F is not always false.

5 - Question

. A compound proposition that is neither a tautology nor a contradiction is called a ___________
a) Contingency
b) Equivalence
c) Condition
d) Inference

Explanation: Definition of contingency.

6 - Question

¬ (A ∨ q) ∧ (A ∧ q) is a ___________
a) Tautology
c) Contingency
d) None of the mentioned

Explanation: ≡ (¬A ∧ ¬q) ∧ (A ∧ q)
≡ (¬A ∧ A) ∧ (¬q ∧ q)
≡ F ∧ F ≡ F.

7 - Question

(A ∨ ¬A) ∨ (q ∨ T) is a __________
a) Tautology
c) Contingency
d) None of the mentioned

Explanation: ≡ (A ∨ ¬A) ∨ (q ∨ T)
≡ T ∨ T ≡ T.

8 - Question

. A ∧ ¬(A ∨ (A ∧ T)) is always __________
a) True
b) False

Explanation: ≡ A ∧ ¬ (A ∨ (A ∧ T))
≡ A ∧ ¬(A ∨ A)
≡ A ∧ ¬A ≡ F.

9 - Question

. (A ∨ F) ∨ (A ∨ T) is always _________
a) True
b) False

Explanation: ≡ (A ∨ F) ∨ (A ∨ T)
≡ A ∨ T ≡ T.

10 - Question

A → (A ∨ q) is a __________
a) Tautology