Which of the following set is empty?

{x \in R | x^{2} = 9 a n d 2 x = 6}

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{x \in R | x^{2} = 9 a n d 2 x = 4}

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{x \in R | x + 4 = 4}

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{x \in R | 2 x + 1 = 3}

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Solution

The correct option is C ${x \in R | x^{2} = 9 a n d 2 x = 4}$
Option B:
$x \in R | x^{2} = 9$ and $2 x = 4$

$⟹ x^{2} = 9 ⟹ x = \pm 3$

$⟹ x < - 3$ and $x > 3$ .....(1)

Also
$2 x = 4 ⟹ x = 2$ .....(2)

Clearly, (1) & (2) has nothing in common

Therefore, this is an empty set.

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