JEE Main 2023 (Online) 1st February Evening Shift | Mathematical Reasoning Question 13 | Mathematics | JEE Main - ExamSIDE.com

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This chapter is currently out of syllabus

1

JEE Main 2023 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

+4

-1

Out of Syllabus

Which of the following statements is a tautology?

A

$$\mathrm{p\vee(p\wedge q)}$$

B

$$(\mathrm{p\wedge(p\to q))\to\,\sim q}$$

C

$$\mathrm{p\to (p\wedge (p\to q))}$$

D

$$(\mathrm{p\wedge q)\to(\sim (p)\to q)}$$

2

JEE Main 2023 (Online) 1st February Morning Shift

MCQ (Single Correct Answer)

+4

-1

Out of Syllabus

The negation of the expression $$q \vee \left( {( \sim \,q) \wedge p} \right)$$ is equivalent to

A

$$( \sim \,p) \wedge ( \sim \,q)$$

B

$$( \sim \,p) \vee q$$

C

$$p \wedge ( \sim \,q)$$

D

$$( \sim \,p) \vee ( \sim \,q)$$

3

JEE Main 2023 (Online) 31st January Evening Shift

MCQ (Single Correct Answer)

+4

-1

Out of Syllabus

The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})) \wedge((\mathrm{p} \wedge \mathrm{r}) \Rightarrow \mathrm{q})$ is a tautology, is :

A

2

B

1

C

4

D

3

4

JEE Main 2023 (Online) 31st January Morning Shift

MCQ (Single Correct Answer)

+4

-1

Out of Syllabus

$$(\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))$$ is a tautology

$$(\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$$ is a contradiction.

Then

A

only (S2) is correct

B

both (S1) and (S2) are correct

C

only (S1) is correct

D

both (S1) and (S2) are wrong

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