Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: {$x : x \epsilon N and 2x +1 \ \textgreater \ 10$ }

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 : 2x + 1 > 10}
or, A = {x : 2x > 10 - 1 = 9}
or, A = {x : x > 9/2 }
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 > 9/2}
= {x : x is a natural number and x ≤ 9/2}

or, A’ = {x : x $\in\mathbb{N}$ and x ≤ 9/2}

or, A’ = {1, 2, 3, 4}

Answer 2

Solution :

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

A = { x : x €N and 2x + 1 > 10 }

= { 5,6,7,8,9,..}

[ Since , 2x + 1 > 10

=> 2x > 9

=> x > 9/2

=> x > 4.5 ]

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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' = { 1,2,3,4,5,6,7,....} - { 5,6,7,8,...}

= { 1,2,3,4 }

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