This chapter is currently out of syllabus
1
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+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
$$((P \wedge(\sim R)) \wedge Q) \vee((\sim Q) \wedge((\sim P) \vee R))$$
2
JEE Main 2022 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Which of the following statements is a tautology ?

A
$$((\sim \mathrm{p}) \vee \mathrm{q}) \Rightarrow \mathrm{p}$$
B
$$p \Rightarrow((\sim p) \vee q)$$
C
$$((\sim p) \vee q) \Rightarrow q$$
D
$$q \Rightarrow((\sim p) \vee q)$$
3
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

The conditional statement

$$((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))$$ is :

A
a tautology
B
C
equivalent to $$p \wedge q$$
D
equivalent to $$( \sim p) \vee r$$
4
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Negation of the Boolean statement (p $$\vee$$ q) $$\Rightarrow$$ (($$\sim$$ r) $$\vee$$ p) is equivalent to :

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