1
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.
2
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
If the truth value of the Boolean expression $$\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right)} \right) \to \left( {p \wedge q} \right)$$ is false, then the truth values of the statements p, q, r respectively can be :
A
T F T
B
F F T
C
T F F
D
F T F
3
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Which of the following is the negation of the statement "for all M > 0, there exists x$$\in$$S such that x $$\ge$$ M" ?
A
there exists M > 0, such that x < M for all x$$\in$$S
B
there exists M > 0, there exists x$$\in$$S such that x $$\ge$$ M
C
there exists M > 0, there exists x$$\in$$S such that x < M
D
there exists M > 0, such that x $$\ge$$ M for all x$$\in$$S
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
The compound statement $$(P \vee Q) \wedge ( \sim P) \Rightarrow Q$$ is equivalent to :
A
$$P \vee Q$$
B
$$P \wedge \sim Q$$
C
$$\sim (P \Rightarrow Q)$$
D
$$\sim (P \Rightarrow Q) \Leftrightarrow P \wedge \sim Q$$
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