Math, asked by sijal94, 1 year ago

for any non empty set A, (A')' is equal to ​

Answers

Answered by djkng0
14

(A')'=A

Because,

A'= to except A

and (A')'=A

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Answered by Swarup1998
0

(A')' = A

For any non-empty set A, (A')' = A.

Given:

A non-empty set A

To find:

(A')'

Step-by-step explanation:

Let x ∈ A

Then x ∉ A'

Then x ∈ (A')'

We have: x ∈ A ⇒ x ∈ (A')'

A ⊆ (A')' ... ... (1)

Also, let y ∈ (A')'

Then y ∉ A'

Then y ∈ A

We have: y ∈ (A')' ⇒ y ∈ A

(A')' ⊆ A ... ... (2)

From (1) and (2), we can conclude

(A')' = A

Refer to the attached image for the Venn diagram of (A')' = A.

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