Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: { x : x is a perfect cube}

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 perfect cube }
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 perfect cube }
= {x : x is not a perfect cube}

Answer 2

Solution :

U = { 1,2,3,4,5,6,7,8,9,10,11,....}

A = { x:x is a perfect cube }

= { 1,27, 64, 125,... }

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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

= { 1,23,4,5,6,7,8,9,10,...} - { 1,27,64,125,....}

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

= Set of natural numbers other than

cube numbers }

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