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

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)
2
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

Let $$\Delta$$ $$\in$$ {$$\wedge$$, $$\vee$$, $$\Rightarrow$$, $$\Leftrightarrow$$} be such that (p $$\wedge$$ q) $$\Delta$$ ((p $$\vee$$ q) $$\Rightarrow$$ q) is a tautology. Then $$\Delta$$ is equal to :

A
$$\wedge$$
B
$$\vee$$
C
$$\Rightarrow$$
D
$$\Leftrightarrow$$
3
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Let p, q, r be three logical statements. Consider the compound statements

$${S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)$$ and

$${S_2}:p \to (q \vee r)$$

Then, which of the following is NOT true?

A
If S2 is True, then S1 is True
B
If S2 is False, then S1 is False
C
If S2 is False, then S1 is True
D
If S1 is False, then S2 is False
4
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

Which of the following statement is a tautology?

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