JEE Main 2022 (Online) 28th July Morning Shift | Mathematical Reasoning Question 28 | Mathematics

Let the operations $$*, \odot \in\{\wedge, \vee\}$$. If $$(\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathrm{q})$$ is a tautology, then the ordered pair $$(*, \odot)$$ is :

$$(\vee, \wedge)$$

$$(\vee, \vee)$$

$$(\wedge, \wedge)$$

$$(\wedge, \vee)$$

JEE Main 2022 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

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

$$p$$

$$\sim p$$

$$q$$