1
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
$$\mathrm{p} \Rightarrow((\sim \mathrm{q}) \wedge(\mathrm{r} \vee \mathrm{s}))$$
2
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
$$(\wedge, \vee)$$
3
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
$$\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \,\sim \mathrm{P}$$
4
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
$$\sim q$$
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Medical
NEET