Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: { x : x is a prime 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 a prime 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 a prime number}
= {x : x is not a prime number }

Answer 2

Solution :

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

A = { x:x is a prime number }

= { 2,3,5,7,11,13,17,... }

*******************************************
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,... } - { 2,3,5,7,11,13,17,...}

= { 1,4,68,9,10,12,14,15,16,18,20,...}

= Set of all natural numbers other than

prime numbers

•••••