The Boolean expression $(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$ is equivalent to:

(C) $(p \wedge q) \Rightarrow(r \wedge q)$

(A) $(\mathrm{p} \wedge \mathrm{r}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$

(B) $(\mathrm{q} \wedge \mathrm{r}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$

(D) $(p \wedge q) \Rightarrow(r \vee q)$

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Mathematical Reasoning *

The Boolean expression

(p \land q) \Rightarrow ((r \land q) \land p)

is equivalent to:

Answer: (C)

The given expression

(p \land q) \Rightarrow ((r \land q) \land p)

can be simplified. When

p \land q

is true, the consequent

(r \land q) \land p

requires

r \land q

to be true (since

p

is already true). Thus the implication reduces to: if

p \land q

is true, then

r \land q

must be true, which is exactly

(p \land q) \Rightarrow (r \land q)

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Single correct option