Which of the following is logically equivalent to p ∧ q ?

Question

Which of the following is logically equivalent to p ∧ q ? (A) p arrow ∼ q (B) ∼ p ∨ ∼ q (C) ∼(p arrow ∼ q) (D) ∼(∼ p ∧ ∼ q2)

Tardigrade Admin · Accepted Answer

We have, p arrow q ≅ ∼ p ∨ q ∴ p arrow ∼ q ≅ ∼ p ∨ ∼ q ≅ ∼ (p ∧ q) So, option (a) is not correct ∼ p ∨ ∼ q=∼(p ∧ q) So, option (b) is not correct ∼(p arrow ∼ q)=∼(∼ p ∨ ∼ q)=p ∧ q So, option (c) is incorrect

Q. Which of the following is logically equivalent to $p \land q ?$

$p \to\sim q$

$\sim p \lor \sim q$

$\sim (p \to\sim q)$

$\sim (\sim p \land \sim q^{2})$

We have,
$p \to q ≅\sim p \lor q$
$∴ p \to\sim q ≅\sim p \lor \sim q ≅\sim (p \land q)$
So, option (a) is not correct
$\sim p \lor \sim q =\sim (p \land q)$
So, option (b) is not correct
$\sim (p \to\sim q) =\sim (\sim p \lor \sim q) = p \land q$
So, option (c) is incorrect

Q. Which of the following is logically equivalent to p∧q?

p→∼q

∼p∨∼q

∼(p→∼q)

∼(∼p∧∼q2)