1
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

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
$$q \Rightarrow((\sim p) \vee q)$$
2
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

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 $$( \sim p) \vee r$$
3
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)
4
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
$$\Leftrightarrow$$
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