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

1.

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

Answer»

Let us prove, A’ – B’ = B – A

Now, firstly we need to show

A’ – B’ ⊆ B – A

Suppose, x ∈ A’ – B’

⇒ x ∈ A’ and x ∉ B’

⇒ x ∉ A and x ∈ B (Here, A ∩ A’ = ϕ )

⇒ x ∈ B – A

Since, it is true for all x ∈ A’ – B’

∴ A’ – B’ = B – A

Thus proved.

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