1
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

The statement $$(p \Rightarrow q) \vee(p \Rightarrow r)$$ is NOT equivalent to

A
$$(p \wedge(\sim r)) \Rightarrow q$$
B
$$(\sim q) \Rightarrow((\sim r) \vee p)$$
C
$$p \Rightarrow(q \vee r)$$
D
$$(p \wedge(\sim q)) \Rightarrow r$$
2
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

The statement $$(p \wedge q) \Rightarrow(p \wedge r)$$ is equivalent to :

A
$$q \Rightarrow(p \wedge r)$$
B
$$p\Rightarrow(\mathrm{p} \wedge \mathrm{r})$$
C
$$(\mathrm{p} \wedge \mathrm{r}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$$
D
$$(p \wedge q) \Rightarrow r$$
3
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Let

$$\mathrm{p}$$ : Ramesh listens to music.

$$\mathrm{q}$$ : Ramesh is out of his village.

$$\mathrm{r}$$ : It is Sunday.

$$\mathrm{s}$$ : It is Saturday.

Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as

A
$$((\sim q) \wedge(r \vee s)) \Rightarrow p$$
B
$$(\mathrm{q} \wedge(\mathrm{r} \vee \mathrm{s})) \Rightarrow \mathrm{p}$$
C
$$p \Rightarrow(q \wedge(r \vee s))$$
D
$$\mathrm{p} \Rightarrow((\sim \mathrm{q}) \wedge(\mathrm{r} \vee \mathrm{s}))$$
4
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
$$(\wedge, \vee)$$
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