EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 27 June 2022 Shift 2>Q 77

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IMPORTANT

Earn 100

Which of the following statement is a tautology?

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Important Questions on Mathematical Reasoning

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 28 June 2022 Shift 1>Q 78

Let $p, q, r$ be three logical statements. Consider the compound statements
$S_{1} : ((~ p) \lor q) \lor ((~ p) \lor r)$ and $S_{2} : p \to (q \lor r)$
Then, which of the following is NOT true?

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 28 June 2022 Shift 2>Q 79

The maximum number of compound propositions, out of

p \lor r \lor s, p \lor r \lor ~ s, p \lor ~ q \lor s

,

~ p \lor ~ r \lor s, ~ p \lor ~ r \lor ~ s, ~ p \lor q \lor ~ s,

q \lor r \lor ~ s, q \lor ~ r \lor ~ s, ~ p \lor ~ q \lor ~ s

that can be made simultaneously true by an assignment of the truth values to

p, q, r

and

s

, is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 29 June 2022 Shift 1>Q 80

Let

Δ \in \{\land, \lor, \Rightarrow, \Leftrightarrow\}

be such that

(p \land q) Δ ((p \lor q) \Rightarrow q)

is a tautology. Then

Δ

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 29 June 2022 Shift 2>Q 81

Negation of the Boolean statement

(p \lor q) \Rightarrow ((~ r) \lor p)

is equivalent to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 25 July 2022 Shift 1>Q 82

Which of the following statements is a tautology?

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 25 July 2022 Shift 2>Q 83

Consider the following statements:

$P :$ Ramu is intelligent.

$Q :$ Ramu is rich.

$R :$ Ramu is not honest.

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 26 July 2022 Shift 1>Q 84

The statement

(~ (p \Leftrightarrow ~ q)) \land q

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Mathematical Reasoning>JEE Main - 26 July 2022 Shift 2>Q 85

Negation of the Boolean expression

p \leftrightarrow (q \to p)

is