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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

If x = 6 and y = - 2 then x - 2y = 9. The contrapositive of this...

If

x = 6

and

y = - 2

then

x - 2y = 9.

The contrapositive of this statement is

Options

AIf $x - 2y \ne 9$ then $x \ne 6$ or $y \ne - 2$
BIf $x - 2y \ne 9$ then $x \ne 6$ and $y \ne - 2$
CIf $x - 2y = 9$ then $x = 6$ and $y = - 2$
DNone of these

Correct answer

A. If $x - 2y \ne 9$ then $x \ne 6$ or $y \ne - 2$

Step-by-step solution

Let

p, q, r

be the three statements such that

p: x = 6, q: y = - 2 and r: x - 2y = 9

Here given statement is \left(p ∧ q\right)\to r

and its contrapositive is

r \to \left(p ∧ q\right)
i.e.

∼ r \to \left(∼ p ∨ ∼ q\right)

i.e. if

x - 2y \ne 9

then

x \ne 6

or

y \ne - 2

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