Given below are two statements one is labelled as assertion A and the other is…
2022
Given below are two statements one is labelled as assertion A and the other is labelled as Reason R:
Assertion A: P′
Reason R: (r → Q′, r → S, S → Q′, P → Q)
In the light of above statement, choose the correct answer from the options given below:
- A.
Both A and R are True and R is the correct explanation of R
- B.
Both A and R are True and R is not the correct explanation of R
- C.
A is true but R is false
- D.
A is false but R is true
Attempted by 31 students.
Show answer & explanation
Correct answer: A
Step 1: Work from implications
From (4)
P→Q
Contrapositive:
Q′→P′
So if we can prove Q′ is true, then P′ must be true.
Step 2: Try to derive Q′
We have:
r→Q′...(1)
r → s ...(2)
s → Q' ...(3)
From (2) and (3):
r→S
S→Q′
⇒r→Q′
(which matches (1), so consistent)
Now key logic idea
All premises in R consistently imply:
Q′ must hold in the system
Because every path leads to Q′:
If r true → Q′
If r true → S → Q′
Hence R guarantees:
Q′ is logically forced
Step 3: Deduce Assertion
We already had:
Q′→P′
and R gives Q′
∴P'
Conclusion
Assertion A ( P′ ) → True
Reason R → True
R correctly explains A
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