QJEEM23Ma9cca: JEE Main 2023 Mathematics - Class 11 JEEM23Ma9cca Solution: Among the statements (S1) : ( p ⇒ q ) ∨ ( ( ∼ p ) ∧ q ) is a…

Question

Verified Solution • 2025–26 Session moderate

Among the statements

(S1) : $(p \Rightarrow q) \lor ((\sim p) \land q)$ is a tautology

(S2) : $(q \Rightarrow p) \Rightarrow ((\sim p) \land q)$ is a contradiction

Accepted Answer

(S1) :

(p \Rightarrow q) \lor ((\sim p) \land q)

\begin{array}{cccccc} P & Q & \sim p & \sim p \land q & p \Rightarrow q & \begin{matrix} (p \Rightarrow q) \lor \\ (\sim p \land q) \end{matrix} \\ T & T & F & F & T & T \\ T & F & F & F & F & F \\ F & T & T & T & T & T \\ F & F & T & F & T & T \end{array}

Here, for every value of components compound statement (last column) are not true. Hence,

S_1

is not a tautology.

S_2:(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)

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