Let *, square ∈ ∧, ∨ be such that the Boolean expression ( p * ∼ q ) ⇒ ( p square q ) is a tautology. Then :

Question

Let *, square ∈ ∧, ∨ be such that the Boolean expression ( p * ∼ q ) ⇒ ( p square q ) is a tautology. Then : (A) *=∨, square=∨ (B) *=∧, square=∧ (C) *=∧, square=∨ (D) *=∨, square=∧

Tardigrade Admin · Accepted Answer

p q ∼ q p ∧ ∼ q p ∨ q ( p ∧ ∼ q ) arrow( p ∨ q ) T T F F T T T F T T T T F T F F T T F F T F F T

$p$	$q$	$\sim q$	$p \land \sim q$	$p \lor q$	$(p \land \sim q) \to (p \lor q)$
T	T	F	F	T	T
T	F	T	T	T	T
F	T	F	F	T	T
F	F	T	F	F	T

Q. Let $, □ \in {\land, \lor}$ be such that the Boolean expression $(p \sim q) \Rightarrow (p □ q)$ is a tautology. Then :

$* = \lor, □ = \lor$

$* = \land, □ = \land$

$* = \land, □ = \lor$

$* = \lor, □ = \land$

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

T T F F T T

T F T T T T

F T F F T T

F F T F F T

Q. Let ∗,□∈{∧,∨} be such that the Boolean expression (p∗∼q)⇒(p□q) is a tautology. Then :

∗=∨,□=∨

∗=∧,□=∧

∗=∧,□=∨

∗=∨,□=∧