Question

If [A=X]X2=16 and 2x+3=5} is not a empty set.why?

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Answer 1

$\underline{\pink{ Empty \:set : }}$

A set which doesn't contain any element is called empty or a Null or a void set .

$Given \:set \: A = \{ x: x^{2} = 16 \: and \: 2x + 3 = 5 \}$

$Here, i) x^{2} = 16\\ \implies x = \pm \sqrt{16} \\\implies x = \pm \sqrt{4^{2}} \\\implies x = \pm 4$

$ii) 2x + 3 = 5 \\\implies 2x = 5 - 3 \\\implies 2x = 2 \\\implies x = \frac{2}{2} \\\implies x = 1$

Therefore.,

$\red{ Set \: A } \green { = \{ -4, 1 , 4 \} }$

$Set \: A \: have \: 4 \: elements \: in \:it$

$\blue{ A \: is \: not \: an \: empty \: set }$

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