1
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Consider the following statements:

A : Rishi is a judge.

B : Rishi is honest.

C : Rishi is not arrogant.

The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

A
B $$\to$$ (A $$\vee$$ C)
B
($$\sim$$B) $$\wedge$$ (A $$\wedge$$ C)
C
B $$\to$$ (($$\sim$$A) $$\vee$$ ($$\sim$$C))
D
B $$\to$$ (A $$\wedge$$ C)
2
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The number of choices for $$\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \}$$, such that

$$(p\Delta q) \Rightarrow ((p\Delta \sim q) \vee (( \sim p)\Delta q))$$ is a tautology, is :

A
1
B
2
C
3
D
4
3
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Which of the following is equivalent to the Boolean expression p $$\wedge$$ $$\sim$$ q ?
A
$$\sim$$ (q $$\to$$ p)
B
$$\sim$$ p $$\to$$ $$\sim$$ q
C
$$\sim$$ (p $$\to$$ $$\sim$$ q)
D
$$\sim$$ (p $$\to$$ q)
4
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Negation of the statement (p $$\vee$$ r) $$\Rightarrow$$ (q $$\vee$$ r) is :
A
p $$\wedge$$ $$\sim$$ q $$\wedge$$ $$\sim$$ r
B
$$\sim$$ p $$\wedge$$ q $$\wedge$$ $$\sim$$ 4
C
$$\sim$$ p $$\wedge$$ q $$\wedge$$ r
D
p $$\wedge$$ q $$\wedge$$ r
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