JEE Main 2022 (Online) 27th July Evening Shift | Mathematical Reasoning Question 29 | Mathematics

If the truth value of the statement $$(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$$ is F, then the truth value of which of the following is $$\mathrm{F}$$ ?

$$\mathrm{P} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{R}$$

$$\mathrm{R} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{P}$$

$$\sim(\mathrm{P} \vee \mathrm{Q}) \rightarrow \sim \mathrm{R}$$

$$\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \,\sim \mathrm{P}$$

JEE Main 2022 (Online) 27th July Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

$$(p \wedge r) \Leftrightarrow(p \wedge(\sim q))$$ is equivalent to $$(\sim p)$$ when $$r$$ is

$$p$$

$$\sim p$$

$$q$$

$$\sim q$$

JEE Main 2022 (Online) 26th July Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Negation of the Boolean expression $$p \Leftrightarrow(q \Rightarrow p)$$ is

$$(\sim p) \wedge q$$

$$p \wedge(\sim q)$$

$$(\sim p) \vee(\sim q)$$

$$(\sim p) \wedge(\sim q)$$

JEE Main 2022 (Online) 26th July Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

The statement $$(\sim(\mathrm{p} \Leftrightarrow \,\sim \mathrm{q})) \wedge \mathrm{q}$$ is :

a tautology

a contradiction

equivalent to $$(p \Rightarrow q) \wedge q$$

equivalent to $$(p \Rightarrow q) \wedge p$$

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