Discrete Mathematics Questions and Answers – Logics – Tautologies and Contradictions

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This set of Discrete Mathematics Questions and Answers for Experienced people focuses on “Logics – Tautologies and Contradictions”.

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

Answer: a
Explanation: Tautology is always true.
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2. A compound proposition that is always ___________ is called a contradiction.
a) True
b) False
View Answer

Answer: b
Explanation: 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
View Answer

Answer: c
Explanation: 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
View Answer

Answer: b
Explanation: 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
View Answer

Answer: a
Explanation: Definition of contingency.
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6. ¬ (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. (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. 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. (A ∨ F) ∨ (A ∨ T) is always _________
a) True
b) False
View Answer

Answer: a
Explanation: ≡ (A ∨ F) ∨ (A ∨ T)
≡ A ∨ T ≡ T.
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10. 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.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn