1
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
2
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
$$(p \wedge q) \wedge ( \sim p \wedge q))$$
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

The boolean expression $$( \sim (p \wedge q)) \vee q$$ is equivalent to :

A
$$q \to (p \wedge q)$$
B
$$p \to q$$
C
$$p \to (p \to q)$$
D
$$p \to (p \vee q)$$
4
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

Let r $$\in$$ {p, q, $$\sim$$p, $$\sim$$q} be such that the logical statement

r $$\vee$$ ($$\sim$$p) $$\Rightarrow$$ (p $$\wedge$$ q) $$\vee$$ r

is a tautology. Then r is equal to :

A
p
B
q
C
$$\sim$$p
D
$$\sim$$q
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