JEE Main 2021 (Online) 24th February Evening Shift | Mathematical Reasoning Question 70 | Mathematics

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?

(b) is a tautology but not (a).

(a) and (b) both are not tautologies.

(a) and (b) both are tautologies.

(a) is a tautology but not (b).

JEE Main 2021 (Online) 24th February Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

The statement among the following that is a tautology is :

$$B \to \left[ {A \wedge \left( {A \to B} \right)} \right]$$

$$\left[ {A \wedge \left( {A \to B} \right)} \right] \to B$$

$$\left[ {A \wedge \left( {A \vee B} \right)} \right]$$

$$\left[ {A \vee \left( {A \wedge B} \right)} \right]$$

JEE Main 2020 (Online) 6th September Evening Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

Consider the statement :
‘‘For an integer n, if n³ – 1 is even, then n is odd.’’
The contrapositive statement of this statement is :

For an integer n, if n is even, then n³ – 1 is even.

For an integer n, if n³ – 1 is not even, then n is not odd.

For an integer n, if n is odd, then n³ – 1 is even.

For an integer n, if n is even, then n³ – 1 is odd.

JEE Main 2020 (Online) 6th September Morning Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

The negation of the Boolean expression p $$ \vee $$ (~p $$ \wedge $$ q) is equivalent to :

$$p \wedge \sim q$$

$$ \sim $$$$p \vee \sim q$$

$$ \sim p \wedge q$$

$$ \sim p \wedge \sim q$$

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