This chapter is currently out of syllabus
1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus

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

A
$$p$$
B
$$\sim p$$
C
$$q$$
D
$$\sim q$$
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1
Out of Syllabus

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
$$(\sim p) \wedge(\sim q)$$
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1
Out of Syllabus

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

A
a tautology
B
C
equivalent to $$(p \Rightarrow q) \wedge q$$
D
equivalent to $$(p \Rightarrow q) \wedge p$$
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1
Out of Syllabus

Consider the following statements:

P : Ramu is intelligent.

Q : Ramu is rich.

R : Ramu is not honest.

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

A
$$((P \wedge(\sim R)) \wedge Q) \wedge((\sim Q) \wedge((\sim P) \vee R))$$
B
$$((P \wedge R) \wedge Q) \vee((\sim Q) \wedge((\sim P) \vee(\sim R)))$$
C
$$((P \wedge R) \wedge Q) \wedge((\sim Q) \wedge((\sim P) \vee(\sim R)))$$
D
$$((P \wedge(\sim R)) \wedge Q) \vee((\sim Q) \wedge((\sim P) \vee R))$$
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