Question

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

Answer 1

(v) (A – B) ∪ (A ∩ B) = A

Consider LHS (A – B) ∪ (A ∩ B)

Suppose, x ∈ A

Now either x ∈ (A – B) or x ∈ (A ∩ B)

⇒ x ∈ (A – B) ∪ (A ∩ B)

∴ A ⊂ (A – B) ∪ (A ∩ B)…. (1)

Conversely,

Suppose x ∈ (A – B) ∪ (A ∩ B)

⇒ x ∈ (A – B) or x ∈ (A ∩ B)

⇒ x ∈ A and x ∉ B or x ∈ B

⇒ x ∈ A

(A – B) ∪ (A ∩ B) ⊂ A………. (2)

∴ From the equation (1) and (2), We get

(A – B) ∪ (A ∩ B) = A

Thus proved

Answer 2

Answer:

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

Step-by-step explanation: