Consider the following statements : (a) False ? True (b) If α ? (β ∧ γ) then α…
2018
Consider the following statements :
(a) False ? True
(b) If α ? (β ∧ γ) then α ? β and α ? γ.
Which of the following is correct with respect to the above statements?
- A.
Both statement a and statement b are false
- B.
Statement a is true and statement b is false
- C.
Statement a is false and statement b is true
- D.
Both statement a and statement b are true
Attempted by 140 students.
Show answer & explanation
Correct answer: D
Answer: Both statements are true.
Explanation:
Statement (a): A contradiction (False) has no models, so the entailment relation is vacuously satisfied for any conclusion. Therefore False entails True. Example: from p ∧ ¬p you can entail any formula q.
Statement (b): If every model of α satisfies the conjunction β ∧ γ, then every model of α satisfies γ as well. Hence α entails γ. This is the entailment form of conjunction elimination.
Conclusion: Both statements are true for the reasons above.
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