Which of the following statements is a tautology?

Plotting the truth table of the following option we have,

$p$	$q$	$~ p$	$~ q$	$~ p ∨ q$
$T$	$T$	$F$	$F$	$T$
$T$	$F$	$F$	$T$	$F$
$F$	$T$	$T$	$F$	$T$
$F$	$F$	$T$	$T$	$T$

We know that, $A ⇒ B$ is only false when $A$ is true and $B$ is false, now using this rule and above table we will make truth table of options,

$\left(\left(~ p\right) ∨ q\right) ⇒ p$

$p ⇒ \left(\left(~ p\right) ∨ q\right)$

\left(\left(~ p\right) ∨ q\right) ⇒ q$</td> <td>$q ⇒ \left(\left(~ p\right) ∨ q\right)$</td> </tr> <tr> <td>$T$</td> <td>$T$</td> <td>$T$</td> <td>$T$</td> </tr> <tr> <td>$T$</td> <td>$F$</td> <td>$T$</td> <td>$T$</td> </tr> <tr> <td>$F$</td> <td>$T$</td> <td>$T$</td> <td>$T$</td> </tr> <tr> <td>$F$</td> <td>$T$</td> <td>$F$</td> <td>$T$</td> </tr> </tbody></table><p> </p><p>Hence$q ⇒ \left(\left(~ p\right) ∨ q\right) is tautology. Practice Mathematical Reasoning on Quantrex Academy → More from Mathematical Reasoning Negation of p ∧ (q ∧ ~ (p ∧ q)) is JEE Main 2023The statement ( p ∧ ( ~ q ) ) ∨ ( ( ~ p ) ∧ q ) ∨ ( ( ~ p ) ∧ ( ~ q ) ) is equivalent to… JEE Main 2023The negation of the statement ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A is JEE Main 2023Among the two statements ( S _ 1 ): (p ⇒ q) ∧ (p ∧ (~ q)) is a contradiction and ( S _ 2… JEE Main 2023The converse of ((~ p) ∧ q) ⇒ r is JEE Main 2023The number of ordered triplets of the truth values of p, q and r such that the truth… JEE Main 2023The statement ~ [p ∨ (~ (p ∧ q))] is equivalent to JEE Main 2023The negation of the statement (p ∨ q) ∧ (q ∨ (~ r)) is JEE Main 2023The negation of ( p ∧ ( - q ) ) ∨ ( - p ) is equivalent to JEE Main 2023Negation of (p → q) → (q → p) is JEE Main 2023Among the statements (S1): (p ⇒ q) ∨ ((~ p) ∧ q) is a tautology (S2): (q ⇒ p) ⇒ ((~ p) ∧… JEE Main 2023Statement ( P ⇒ Q ) ∧ ( R ⇒ Q ) is logically equivalent to JEE Main 2023Which of the following statements is a tautology? JEE Main 2023The negation of the expression q ∨ ( ( ~ q ) ∧ p ) is equivalent to JEE Main 2023The number of values of r ∈ \ p, q, ~ p, ~ q\ for which ((p ∧ q) ⇒ (r ∨ q) ∧ ( (p ∧ r) ⇒… JEE Main 2023Consider: (S1): (p ⇒ q) ∨ (p ∧ (~ q)) is a tautology. (S2): ((~ p) ⇒ (~ q)) ∧ ((~ p) ∨ q)… JEE Main 2023 Full Mathematical Reasoning list Mathematical Reasoning JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs