1
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
Let *, ▢ $$\in$${$$\wedge$$, $$\vee$$} be such that the Boolean expression (p * $$\sim$$ q) $$\Rightarrow$$ (p ▢ q) is a tautology. Then :
A
* = $$\vee$$, ▢ = $$\vee$$
B
* = $$\wedge$$, ▢ = $$\wedge$$
C
* = $$\wedge$$, ▢ = $$\vee$$
D
* = $$\vee$$, ▢ = $$\wedge$$
2
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
The Boolean expression (p $$\wedge$$ q) $$\Rightarrow$$ ((r $$\wedge$$ q) $$\wedge$$ p) is equivalent to :
A
(p $$\wedge$$ q) $$\Rightarrow$$ (r $$\wedge$$ q)
B
(q $$\wedge$$ r) $$\Rightarrow$$ (p $$\wedge$$ q)
C
(p $$\wedge$$ q) $$\Rightarrow$$ (r $$\vee$$ q)
D
(p $$\wedge$$ r) $$\Rightarrow$$ (p $$\wedge$$ q)
3
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
The statement (p $$\wedge$$ (p $$\to$$ q) $$\wedge$$ (q $$\to$$ r)) $$\to$$ r is :
A
a tautology
B
equivalent to p $$\to$$ $$\sim$$ r
C
a fallacy
D
equivalent to q $$\to$$ $$\sim$$ r
4
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
Consider the two statements :

(S1) : (p $$\to$$ q) $$\vee$$ ($$\sim$$ q $$\to$$ p) is a tautology .

(S2) : (p $$\wedge$$ $$\sim$$ q) $$\wedge$$ ($$\sim$$ p $$\wedge$$ q) is a fallacy.

Then :
A
only (S1) is true.
B
both (S1) and (S2) are false.
C
both (S1) and (S2) are true.
D
only (S2) is true.
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