Question

AnBis not equal to non emty set then n (B-A)=​

Answer 1

Let M = (A ∩ B)' and N = A' U B'

Let x be an arbitrary element of M then x ∈ M ⇒ x ∈ (A ∩ B)'

$⇒ x ∉ (A ∩ B) \\ ⇒ x ∉ A\: or\: x ∉ B \\ ⇒ x ∈ A' or x ∈ B' \\ ⇒ x ∈ A' U B' \\ ⇒ x ∈ N$

Therefore, M ⊂ N …………….. (i)

Again, let y be an arbitrary element of N then y ∈ N ⇒ y ∈ A' U B'

⇒ y ∈ A' or y ∈ B'

⇒ y ∉ A or y ∉ B

⇒ y ∉ (A ∩ B)

⇒ y ∈ (A ∩ B)'

⇒ y ∈ M

Therefore, N ⊂ M …………….. (ii)

Now combine (i) and (ii) we get; M = N i.e. (A ∩ B)' = A' U B'