Q39 / 90 · JEE Main 2023 (06 Apr Shift 1) · Mathematics

Statement $(P \Rightarrow Q) \land (R \Rightarrow Q)$ is logically equivalent to

A
$(P \Rightarrow R) \lor (Q \Rightarrow R)$
B
$(P \land R) \Rightarrow Q$
C
$(P \Rightarrow R) \land (Q \Rightarrow R)$
Correct answer
D
$(P \lor R) \Rightarrow Q$

Solution

Given that $(P \Rightarrow Q) \land (R \Rightarrow Q)$
We know that $P \Rightarrow Q \equiv ~ P \lor Q$
$\Rightarrow (~ P \lor Q) \land (~ R \lor Q)$
$\Rightarrow (~ P \land ~ R) \lor Q$
$\Rightarrow ~ (P \lor R) \lor Q$
$\Rightarrow (P \lor R) \Rightarrow Q$
Hence this is the correct option.

Hence, the correct answer is option: 'D'.

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