Given below are two statements : one is labelled as Assertion (A) and the…
2022
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R) :
Assertion (A): \(\bar{p}\)
Reason (R): \(\quad(r \rightarrow \bar{q}, r \vee s, s \rightarrow \bar{q}, p \rightarrow q)\)
In the light of the above statements, choose the correct answer from the options given below :
- A.
Both (A) and (R) are true and (R) is the correct explanation of (A)
- B.
Both (A) and (R) are true but (R) is (NOT) the correct explanation of (A)
- C.
(A) is true but (R) is false
- D.
(A) false but (R) is true
Attempted by 125 students.
Show answer & explanation
Correct answer: A
Explanation: The Assertion is ¬p and the Reason gives the premises r → ¬q, r ∨ s, s → ¬q, and p → q.
From r → ¬q, s → ¬q and r ∨ s we deduce ¬q.
Given p → q and ¬q, by modus tollens we infer ¬p.
Therefore the Assertion ¬p follows from the premises in the Reason, so both the Assertion and the Reason are true and the Reason correctly explains the Assertion.
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