Question

For any set A, (A')' is equal to​

Answer 1

Concept

The complement of set A is a set that contains all of the elements in the universal set but none of them in set A.

Given

Set A

Find

For any set A, (A')' is equal to​ what?

Solution

We can say that complement of complement of a set A equals to the set A.

Hence (A')'= A

Answer 2

Answer:

According to the question ,

we need to show, $A = (A')'$

Let, $S$ be the universal set.

so, by definition if $x \in A \implies x \notin A'$

let, $x \in A \implies x\notin A' \implies x \in S-A' \implies x \in (A')'$

so, $A \subseteq (A')' \: .....(1)$

Similarly,

let, $y \in (A')' \implies y\notin A' \implies y \in S-A' \implies x \in A$

so, $(A')' \subseteq A \: ......(2)$

from $(1) \& (2)$

$A = (A')'$

Hence, we get $A = (A')'$