Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: { x : 2x + 5 = 9 }

Answer 1

Taking the set of natural numbers as the universal set.
so, U = {x : x is a natural number }
Let us assume that A = {x : 2x + 5 = 9}
or, A ={x : 2x = 9 - 5 = 4}
or, A = {x : x = 2}

we have to write complement of set A.

we know, complement of A is the set of all distinct elements or objects that do not belong to A. it is denoted by A' or $A^c$
you can find easily complement of any set using formula, A' = U - A

so, A’ = {x : x is a natural number} - {x : x = 2}
= {x : x is a natural number and x ≠ 2}

or, A’ = {x : x $\in\mathbb{N}-\{2\}$}

Answer 2

Solution :

U = { 1,2,3,4,5,6,7,,...}

A = { x: 2x + 5 = 9 }

= { 2 }

[ Since , 2x + 5 = 9

=> 2x = 9 - 5

=> 2x = 4

=> x = 4/2 = 2 ]

****************************************
Complement of set A is denoted by A'.

A' = U - A

= { x : x€U and x doesn't belongs to A }

*****************************************
Here ,

A' = U - A

= { 1,2,3,4,5,6,7,... } - { 2 }

= { 1,3,4,5,6,7,...}

= Set of natural numbers other than 2

= { x : x € N , x ≠ 2 }

or

= N - { 2 }

•••••••