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Question -

For any two sets A and B, prove that: A‘ – B‘ = B – A



Answer -

To prove, A’ – B’ = B – A
Firstly we need to show
A’ – B’ ⊆ B – A
Let, x ∈ A’ – B’
⇒ x ∈ A’ and x ∉ B’
⇒ x ∉ A and x ∈ B (since, A ∩ A’ = ϕ )
⇒ x ∈ B – A
It is true for all x ∈ A’ – B’
∴ A’ – B’ = B – A
Hence Proved.

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