1
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
The negation of the statement

$$\sim p \wedge (p \vee q)$$ is :
A
$$p \vee \sim q$$
B
$$\sim p \vee q$$
C
$$\sim p \wedge q$$
D
$$p \wedge \sim q$$
2
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
For the statements p and q, consider the following compound statements :

(a) $$( \sim q \wedge (p \to q)) \to \sim p$$

(b) $$((p \vee q) \wedge \sim p) \to q$$

Then which of the following statements is correct?
A
(b) is a tautology but not (a).
B
(a) and (b) both are not tautologies.
C
(a) and (b) both are tautologies.
D
(a) is a tautology but not (b).
3
JEE Main 2021 (Online) 24th February Morning Slot
+4
-1
The statement among the following that is a tautology is :
A
$$B \to \left[ {A \wedge \left( {A \to B} \right)} \right]$$
B
$$\left[ {A \wedge \left( {A \to B} \right)} \right] \to B$$
C
$$\left[ {A \wedge \left( {A \vee B} \right)} \right]$$
D
$$\left[ {A \vee \left( {A \wedge B} \right)} \right]$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Consider the statement :
‘‘For an integer n, if n3 – 1 is even, then n is odd.’’
The contrapositive statement of this statement is :
A
For an integer n, if n is even, then n3 – 1 is even.
B
For an integer n, if n3 – 1 is not even, then n is not odd.
C
For an integer n, if n is odd, then n3 – 1 is even.
D
For an integer n, if n is even, then n3 – 1 is odd.
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