Question

For any two sets A and B, prove that
(i) (A ∪ B) – B = A – B
(ii) A – (A ∩ B) = A – B
(iii) A – (A – B) = A ∩ B

Answer 1

(i) (A ∪ B) – B = A – B

Consider LHS (A ∪ B) – B

= (A – B) ∪ (B – B)

= (A – B) ∪ ϕ (here, B – B = ϕ)

= A – B (here, x ∪ ϕ = x for any set)

= RHS

Thus proved.

(ii) A – (A ∩ B) = A – B

Consider LHS A – (A ∩ B)

= (A – A) ∩ (A – B)

= ϕ ∩ (A – B) (here, A - A = ϕ)

= A – B

= RHS

Thus proved.

(iii) A – (A – B) = A ∩ B

Consider LHS A – (A – B)

Suppose, x ∈ A – (A – B) = x ∈ A and x ∉ (A – B)

x ∈ A and x ∉ (A ∩ B)

= x ∈ A ∩ (A ∩ B)

= x ∈ (A ∩ B)

= (A ∩ B)

= RHS

Thus proved.

Answer 2

Answer:

sister plz refer above answer...............................

Step-by-step explanation: