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
View Answer
Answer: a
Explanation: Tautology is always true.
2 - Question
A compound proposition that is always ___________ is called a contradiction.
a) True
b) False
View Answer
Answer: b
Explanation: Contradiction is always 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
View Answer
Answer: c
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
View Answer
Answer: b
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
View Answer
Answer: a
Explanation: Definition of contingency.
6 - Question
¬ (A ∨ q) ∧ (A ∧ q) is a ___________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
View Answer
Answer: b
Explanation: ≡ (¬A ∧ ¬q) ∧ (A ∧ q)
≡ (¬A ∧ A) ∧ (¬q ∧ q)
≡ F ∧ F ≡ F.
7 - Question
(A ∨ ¬A) ∨ (q ∨ T) is a __________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
View Answer
Answer: a
Explanation: ≡ (A ∨ ¬A) ∨ (q ∨ T)
≡ T ∨ T ≡ T.
8 - Question
. A ∧ ¬(A ∨ (A ∧ T)) is always __________
a) True
b) False
View Answer
Answer: b
Explanation: ≡ A ∧ ¬ (A ∨ (A ∧ T))
≡ A ∧ ¬(A ∨ A)
≡ A ∧ ¬A ≡ F.
9 - Question
. (A ∨ F) ∨ (A ∨ T) is always _________
a) True
b) False
View Answer
Answer: a
Explanation: ≡ (A ∨ F) ∨ (A ∨ T)
≡ A ∨ T ≡ T.
10 - Question
A → (A ∨ q) is a __________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
View Answer
Answer: a
Explanation: ≡ A → (A ∨ q)
≡ ¬A ∨ (A ∨ q)
≡ (A ∨ ¬A) ∨ q
≡ T ∨ q ≡ T.