Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20209 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2020 · 9 January · Morning Shift · Mathematics · Mathematical Reasoning

Negation of the statement: 5 is an integer or 5 is irrational is:

Negation of the statement:

\sqrt{5}

is an integer or

5

is irrational is:

Options

A $\sqrt{5}$ is not an integer $5$ is not irrational
B $\sqrt{5}$ is not an integer and $5$ is not irrational
C $\sqrt{5}$ is irrational or $5$ is an integer
D $\sqrt{5}$ is an integer and $5$ irrational

Correct answer

B. $\sqrt{5}$ is not an integer and $5$ is not irrational

Step-by-step solution

Using

~ \left(p ∨ q\right) = ~ p ∧ ~ q

, we get negation of given statement as

\sqrt{5}

is not an integer and

5

is not irrational Number.

Practice Mathematical Reasoning on Quantrex Academy →

More from Mathematical Reasoning

Negation of p ∧ (q ∧ ~ (p ∧ q)) is JEE Main 2023 The statement ( p ∧ ( ~ q ) ) ∨ ( ( ~ p ) ∧ q ) ∨ ( ( ~ p ) ∧ ( ~ q ) ) is equivalent to… JEE Main 2023 The negation of the statement ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A is JEE Main 2023 Among the two statements ( S _ 1 ): (p ⇒ q) ∧ (p ∧ (~ q)) is a contradiction and ( S _ 2… JEE Main 2023 The converse of ((~ p) ∧ q) ⇒ r is JEE Main 2023 The number of ordered triplets of the truth values of p, q and r such that the truth… JEE Main 2023 The statement ~ [p ∨ (~ (p ∧ q))] is equivalent to JEE Main 2023 The negation of the statement (p ∨ q) ∧ (q ∨ (~ r)) is JEE Main 2023 The negation of ( p ∧ ( - q ) ) ∨ ( - p ) is equivalent to JEE Main 2023 Negation of (p → q) → (q → p) is JEE Main 2023 Among the statements (S1): (p ⇒ q) ∨ ((~ p) ∧ q) is a tautology (S2): (q ⇒ p) ⇒ ((~ p) ∧… JEE Main 2023 Statement ( P ⇒ Q ) ∧ ( R ⇒ Q ) is logically equivalent to JEE Main 2023 Which of the following statements is a tautology? JEE Main 2023 The negation of the expression q ∨ ( ( ~ q ) ∧ p ) is equivalent to JEE Main 2023 The number of values of r ∈ \ p, q, ~ p, ~ q\ for which ((p ∧ q) ⇒ (r ∨ q) ∧ ( (p ∧ r) ⇒… JEE Main 2023 Consider: (S1): (p ⇒ q) ∨ (p ∧ (~ q)) is a tautology. (S2): ((~ p) ⇒ (~ q)) ∧ ((~ p) ∨ q)… JEE Main 2023 Full Mathematical Reasoning list Mathematical Reasoning JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs