If the truth value of the statement (P ∧ (~ R) ) → ((~ R) ∧ Q) is F...

We know that A \to B$is false, when A$ is true and $B$ is false

So, for \left(P ∧ \left(~ R\right)\right) \to \left(\left(~ R\right)∧ Q\right) to be false, $P ∧$\left(~ R\right)$should be true and \left(~ R\right) ∧ Q$ is false.

i.e $P$ is true, $R$ is false and $Q$ is false.

A$</td> <td>$B$</td> <td>A \to B$

T$</td> <td>T</td> <td>T</td> </tr> <tr> <td>T</td> <td>F</td> <td>F</td> </tr> <tr> <td>F</td> <td>T</td> <td>T</td> </tr> <tr> <td>F</td> <td>F</td> <td>T</td> </tr> </tbody></table><p>Now, </p><p>for$P ∨ Q \to ~ R$is$F \to T ≡ T$</p><p>$R ∨ Q \to ~ P$is$F \to F ≡ T$</p><p>$~ $\left(P ∨ Q\right)$ \to ~ R$is$T \to T ≡ T$</p><p>$~ $\left(R ∨ Q\right)$ \to ~ P$is$T \to F ≡ F$</p></blockquote>$ 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