Question

Taking the set of natural numbers as the universal set, write down the complements of the given set: {x : x + 5 =8 }

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 + 5 = 8}
or, A = {x : x = 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 = 3}
= {x : x is a natural number and x ≠ 3}

or, A' = {x : x $\in\mathbb{N}-\{3\}$}