If the Boolean expression $(p \oplus q) \wedge(\sim p \Theta q)$ is equivalent to $p \wedge q$, where $\oplus$, $\Theta \in\{\wedge, \vee\}$, then the ordered pair $(\oplus, \Theta)$ is :

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Mathematical Reasoning *

If the Boolean expression

(p \oplus q) \land (\sim p Θ q)

is equivalent to

p \land q

, where

\oplus

Θ \in {\land, \lor}

, then the ordered pair

(\oplus, Θ)

is :

Answer: (C)

Test the combination

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

. Distributing gives

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

. The first bracket contains

p \land \sim p

, which is false, and the second simplifies to

p \land q

. What survives is exactly

p \land q

, so the pair of connectives that works is

\land

followed by

\lor

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option