1
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
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

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

A
(p $$\Delta$$ r) $$\vee$$ q
B
(p $$\Delta$$ r) $$\wedge$$ q
C
(p $$\wedge$$ r) $$\Delta$$ q
D
(p $$\nabla$$ r) $$\wedge$$ q
3
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

The negation of the Boolean expression (($$\sim$$ q) $$\wedge$$ p) $$\Rightarrow$$ (($$\sim$$ p) $$\vee$$ q) is logically equivalent to :

A
$$p \Rightarrow q$$
B
$$q \Rightarrow p$$
C
$$\sim (p \Rightarrow q)$$
D
$$\sim (q \Rightarrow p)$$
4
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Consider the following two propositions:

$$P1: \sim (p \to \sim q)$$

$$P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)$$

If the proposition $$p \to (( \sim p) \vee q)$$ is evaluated as FALSE, then :

A
P1 is TRUE and P2 is FALSE
B
P1 is FALSE and P2 is TRUE
C
Both P1 and P2 are FALSE
D
Both P1 and P2 are TRUE
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