Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: {x : x is a positive multiple of 3 }

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 a positive multiple of 3}
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 a positive multiple of 3}
= {x : x is not a positive multiple of 3}

Answer 2

Solution :

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

A = { x:x is a positive multiple of 3 }

= { 3,6,9,12,15,18,21,....}

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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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A' = U - A

= { 1,2,3,4,5,6,....} - { 3,6,9,12,15,....}

= { 1,2,4,5,7,8,10,11,13,...}

= Set of all natural numbers other than

positive multiples of 3

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