Q40 / 90 · JEE Main 2016 (03 Apr) · Mathematics

The Boolean Expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to

Correct answer
A
$p \lor q$
B
$p \lor \sim q$
C
$\sim p \land q$
D
$p \land q$

Solution

(p \land \sim q) \lor q \lor (\sim p \land q)

Set equivalent

= (A \cap \bar{B}) \cup (\bar{A} \cap B) \cup B

= ((A \cup B) - (A \cap B)) \cup B

= A \cup B

Hence answer is

p \lor q

.

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

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