The negation of compound statement (p ∧ q) Leftrightarrow (r ∧ q) is equivalent to

Question

The negation of compound statement (p ∧ q) Leftrightarrow (r ∧ q) is equivalent to (A) [(p ∧ q) ∨ (q ∧ r)]∧ [∼ (p ∧ q ∧ r)] (B) (.p∧ q∧ r.)∨ [.(.p∧ q.)∨ (.q∧ r.)]. (C) ∼ (p ∧ q ∧ r)∨ [(p ∧ q) ∨ (q ∧ r)] (D) none of these

Tardigrade Admin · Accepted Answer

(p ∧ q) Leftrightarrow (r ∧ q) is equivalent to [∼ (p ∧ q) ∨ (r ∧ q)]∧ [∼ (r ∧ q) ∨ (p ∧ q)]

Q. The negation of compound statement $(p \land q) \Leftrightarrow (r \land q)$ is equivalent to

$[(p \land q) \lor (q \land r)] \land [\sim (p \land q \land r)]$

$(p \land q \land r) \lor [(p \land q) \lor (q \land r)]$

$\sim (p \land q \land r) \lor [(p \land q) \lor (q \land r)]$

none of these

$(p \land q) \Leftrightarrow (r \land q)$ is equivalent to
$[\sim (p \land q) \lor (r \land q)] \land [\sim (r \land q) \lor (p \land q)]$

Q. The negation of compound statement (p∧q)⇔(r∧q) is equivalent to

[(p∧q)∨(q∧r)]∧[∼(p∧q∧r)]

(p∧q∧r)∨[(p∧q)∨(q∧r)]

∼(p∧q∧r)∨[(p∧q)∨(q∧r)]