Discrete Mathematics Questions and Answers for Experienced people on “Logics – Tautologies and Contradictions”.
1. A compound proposition that is always ___________ is called a tautology.
a) True
b) False
Answer: a
Clarification: Tautology is always true.
2. A compound proposition that is always ___________ is called a contradiction.
a) True
b) False
Answer: b
Clarification: Contradiction is always false.
3. 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
Answer: c
Clarification: A ∨ ¬A is always true.
4. 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
Answer: b
Clarification: A ∨ F is not always false.
5. A compound proposition that is neither a tautology nor a contradiction is called a ___________
a) Contingency
b) Equivalence
c) Condition
d) Inference
Answer: a
Clarification: Definition of contingency.
6. ¬ (A ∨ q) ∧ (A ∧ q) is a ___________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
Answer: b
Clarification: ≡ (¬A ∧ ¬q) ∧ (A ∧ q)
≡ (¬A ∧ A) ∧ (¬q ∧ q)
≡ F ∧ F ≡ F.
7. (A ∨ ¬A) ∨ (q ∨ T) is a __________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
Answer: a
Clarification: ≡ (A ∨ ¬A) ∨ (q ∨ T)
≡ T ∨ T ≡ T.
8. A ∧ ¬(A ∨ (A ∧ T)) is always __________
a) True
b) False
Answer: b
Clarification: ≡ A ∧ ¬ (A ∨ (A ∧ T))
≡ A ∧ ¬(A ∨ A)
≡ A ∧ ¬A ≡ F.
9. (A ∨ F) ∨ (A ∨ T) is always _________
a) True
b) False
Answer: a
Clarification: ≡ (A ∨ F) ∨ (A ∨ T)
≡ A ∨ T ≡ T.
10. A → (A ∨ q) is a __________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
Answer: a
Clarification: ≡ A → (A ∨ q)
≡ ¬A ∨ (A ∨ q)
≡ (A ∨ ¬A) ∨ q
≡ T ∨ q ≡ T.