Question

Prove Theoretically:AU(B-A)=AUB

Answer 1

Answer:

We have to prove that : (A-B) U (B-A) = (A∪B) - (A∩B)

Step-by-step explanation:

Proof:

Let,  x ∈ (A-B) U (B-A)

⇒ x ∈ (A-B) or x ∈ (B-A)

⇒  x ∈ A But x ∉ B  or  x ∈ B but x ∉ A,

⇒ x ∈ A or x ∈ B

⇒ x ∈ (A∪B)

⇒ x ∈ (A∪B) - (A∩B)

Since here x represents the arbitrary element of the set (A-B) U (B-A).

Thus, (A-B) U (B-A) = (A∪B) - (A∩B)

Hence, proved.