Question

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

Answer 1

(iv) A ∪ (B – A) = A ∪ B

Consider LHS A ∪ (B – A)

Suppose, x ∈ A ∪ (B – A) ⇒ x ∈ A or x ∈ (B – A)

⇒ x ∈ A or x ∈ B and x ∉ A

⇒ x ∈ B

⇒ x ∈ (A ∪ B) (here, B ⊂ (A ∪ B))

This is true for all x ∈ A ∪ (B – A)

∴ A ∪ (B – A) ⊂ (A ∪ B)…… (1)

Conversely,

Suppose x ∈ (A ∪ B) ⇒ x ∈ A or x ∈ B

⇒ x ∈ A or x ∈ (B – A) (here, B ⊂ (A ∪ B))

⇒ x ∈ A ∪ (B – A)

∴ (A ∪ B) ⊂ A ∪ (B – A)…… (2)

From the equation 1 and 2 we get,

A ∪ (B – A) = A ∪ B

Thus proved

Answer 2

Answer:

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

Step-by-step explanation: