1
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

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 :

A
$$(\vee, \wedge)$$
B
$$(\vee, \vee)$$
C
$$(\wedge, \wedge)$$
D
$$(\wedge, \vee)$$
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

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 $$\mathrm{F}$$ ?

A
$$\mathrm{P} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{R}$$
B
$$\mathrm{R} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{P}$$
C
$$\sim(\mathrm{P} \vee \mathrm{Q}) \rightarrow \sim \mathrm{R}$$
D
$$\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \,\sim \mathrm{P}$$
3
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

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

A
$$p$$
B
$$\sim p$$
C
$$q$$
D
$$\sim q$$
4
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

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

A
$$(\sim p) \wedge q$$
B
$$p \wedge(\sim q)$$
C
$$(\sim p) \vee(\sim q)$$
D
$$(\sim p) \wedge(\sim q)$$
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