Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Mathematical Reasoning

Consider the statement: "For an integer n , if n ^ 3 - 1 is even,...

Consider the statement: "For an integer nn, if n3−1{n}^{3} - 1 is even, then nn is odd". The contrapositive statement of this statement is:

Options

  1. AFor an integer nn, if nn is even, then n3−1{n}^{3} - 1 is odd.
  2. BFor an integer nn, if n3−1{n}^{3} - 1 is not even, then nn is not odd.
  3. CFor an integer nn, if nn is even, then n3−1{n}^{3} - 1 is even.
  4. DFor an integer nn, if nn is odd, then n3−1{n}^{3} - 1 is even.

Correct answer

A. For an integer nn, if nn is even, then n3−1{n}^{3} - 1 is odd.

Step-by-step solution

P:n3−1P: {n}^{3} - 1 is even, q:nq: n is odd

contrapositive of p→q= q→ pp \to q = ~ q \to ~ p

⇒⇒ "if nn is not odd then n3−1{n}^{3} - 1 is not even"

⇒⇒For an integer nn if nn is even, then n3−1{n}^{3} - 1 is odd.

Practice Mathematical Reasoning on Quantrex Academy →

More from Mathematical Reasoning

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