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1
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
2
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
$$\sim (P \Rightarrow Q) \Leftrightarrow P \wedge \sim Q$$
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :
A
The match will not be played and weather is not good and ground is wet.
B
If the match will not be played, then either weather is not good or ground is wet.
C
The match will be played and weather is not good or ground is wet.
D
The match will not be played or weather is good and ground is not wet.
4
JEE Main 2021 (Online) 25th July Morning Shift
The Boolean expression $$(p \Rightarrow q) \wedge (q \Rightarrow \sim p)$$ is equivalent to :
$$\sim$$ q
$$\sim$$ p