Negation of the Boolean expression p↔q→p is

Correct answer: (D) ~p∧~q. To find ~p↔q→p We know ~p↔q≡p∧~q∨q∧~p So ~p↔q→p ≡p∧~q→p∨q→p∧~p Now p∧~q→p≡p∧q∧~p≡p∧~p∧q≡c and q→p∧~p≡~q∨p∧~p≡~p∧~q∨p ≡~p∧~q∨~p∧p=~p∧~q Hence ~p↔q→p≡c∨~p∧~q≡~p∧~q

Q47 / 90 · JEE Main 2022 (26 Jul Shift 2) · Mathematics

Negation of the Boolean expression $p \leftrightarrow (q \to p)$ is

A
$(~ p) \land q$
B
$p \land (~ q)$
C
$(~ p) \lor (~ q)$
Correct answer
D
$(~ p) \land (~ q)$

Solution

To find $~ (p \leftrightarrow (q \to p))$
We know $~ (p \leftrightarrow q) \equiv (p \land ~ q) \lor (q \land ~ p)$
So $~ (p \leftrightarrow (q \to p))$
$\equiv (p \land ~ (q \to p)) \lor ((q \to p) \land ~ p)$
Now $(p \land ~ (q \to p)) \equiv p \land (q \land ~ p) \equiv (p \land ~ p) \land q \equiv c$
and $(q \to p) \land ~ p \equiv (~ q \lor p) \land ~ p \equiv ~ p \land (~ q \lor p)$
$\equiv (~ p \land ~ q) \lor (~ p \land p) = ~ p \land ~ q$
Hence $~ (p \leftrightarrow (q \to p)) \equiv c \lor (~ p \land ~ q) \equiv ~ p \land ~ q$

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

Negation of the Boolean expression p↔q→p is

Solution

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Negation of the Boolean expression $p \leftrightarrow (q \to p)$ is