Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: {x : x is an even natural number}

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 : x is an even natural number}
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 is an even natural number }
= {x : x is an odd natural number }



[note : actually, natural numbers are the group of even and odd numbers]

Answer 2

Solution :

Given U = N

= Set of natural numbers

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

A = { x:x is an even natural number }

= { 2,4,6,8,10,....}

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Complement of set A is denoted by A'.

A' = U - A

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

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Here ,

A' = U - A

= { 1,2,3,4,5,...} - { 2,4,6,8,... }

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

= Set of Odd natural numbers

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