for any non empty set A, (A')' is equal to
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(A')'=A
Because,
A'= to except A
and (A')'=A
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(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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