1
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
$$(p \wedge q) \wedge ( \sim p \wedge q))$$
2
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
$$p \to (p \vee q)$$
3
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
4
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
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