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Logical Connectives

The contrapos...

Question

The contrapositive of $2 x + 3 y = 9 \Rightarrow x \neq 4$ is

A

x = 4 \Rightarrow 2 x + 3 y \neq 9

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B

x = 4 \Rightarrow 2 x + 3 y = 9

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C

x \neq 4 \Rightarrow 2 x + 3 y \neq 9

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D

x \neq 4 \Rightarrow 2 x + 3 y = 9

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Solution

The correct option is A $x = 4 \Rightarrow 2 x + 3 y \neq 9$
Let $p \equiv 2 x + 3 y = 9$ , $q \equiv x \neq 4$
We know, contrapositive of $p \to q \equiv \sim q \to\sim p$
So, the contrapositive of $2 x + 3 y = 9 \Rightarrow x \neq 4$ is $x = 4 \Rightarrow 2 x + 3 y \neq 9$

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Logical Connectives

Standard XII Mathematics

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