Question

B = {x : x + 5 = 5} is not an empty set. Why?

Answer 1

Answer:

B = { 0 }

Hence B is not an empty set

Step-by-step explanation:

B = {x : x + 5 = 5}

x + 5 = 5

subtracting 5 from both sides

=> x + 5 - 5 = 5 - 5

=> x = 0

hence B = { 0 }

so B set has one number = 0

=>B is not an empty set

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO EXPLAIN

The reason behind

B = {x : x + 5 = 5} is not an empty set

DEFINITION TO BE MEMORISED

EMPTY SET

A set S is said to be Empty Set if S contains no element

CALCULATION

Here B = { x : x + 5 = 5 }

Now

$\sf{ x + 5 = 5\: }$

$\implies \sf{ x = 0\: }$

$\sf{Hence \: \: B = \{ x : x + 5 = 5 \} = \{ \: 0 \: \}}$

Since B contains the element 0

Hence B is a NON EMPTY SET

# POINTS TO NOTICE

Here { 0 } does not mean it is an empty set

Since 0 itself can be element of a set

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