Question

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


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

Answer 2

Solution :

Given U = set of natural numbers

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

Let A = { x:x is an odd natural number }

= { 1,3,5,7,9,... }

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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

= { 1,2,3,4,5,6,7,.... } - { 1,3,5,7,9,..... }

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

= Set of even natural numbers.

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