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

Correct answer: (C) *=∧, □=∨. Let (p∧~q)→(p∨q) is a tautology. p q ~q p∨q p∧~q p∧~q⇒p∨q T T F T F T T F T T T T F T F T F T F F T F F T All are true so it's a tautology.

Q32 / 90 · JEE Main 2021 (31 Aug Shift 1) · Mathematics

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

A
$* = \lor, □ = \land$
B
$* = \lor, □ = \lor$
Correct answer
C
$* = \land, □ = \lor$
D
$* = \land, □ = \land$

Solution

Let

(p \land ~ q) \to (p \lor q)

is a tautology.

$p$	$q$	$~ q$	$p \lor q$	$p \land ~ q$	$(p \land ~ q) \Rightarrow (p \lor q)$
$T$	$T$	$F$	$T$	$F$	$T$
$T$	$F$	$T$	$T$	$T$	$T$
$F$	$T$	$F$	$T$	$F$	$T$
$F$	$F$	$T$	$F$	$F$	$T$

All are true so it's a tautology.

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

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

Solution

Relevant Questions

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