Question

(A')' is equal to ?​

Answer 1

In sets, A' is a complement of set A.

By properties of sets, (A')' is equal to A.

For your information,

we can show the identity of sets with the Benn Diagram.

Here are some important properties of sets:

• De Morgan's Laws
• Identity of Sets: Idempotent and Dominant
• Complement of Complement

Answer 2

SOLUTION

TO DETERMINE

(A')' =

EVALUATION

We know that for any set A

A' = { x ∈ U : x ∉ A }

Now we show that (A')' = A

Let x ∈ (A')'

⇒ x ∉ A'

⇒ x ∈ A

∴ (A')' ⊆ A

Next suppose that

y ∈ A

⇒ y ∉ A'

⇒y ∈ (A')'

∴ A ⊆ (A')'

Thus from above (A')' = A

FINAL ANSWER

(A')' = A

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