Question

Prove that (AUB)-(AB)=(A-B)u(B-A)​

Answer 1

Answer:

This question is based on set theory. The proof for the following is as follows.

Step-by-step explanation:

Let us consider that  x ∈ (A-B) U (B-A)

Therfore we can write that

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)

In this case, x represents the arbitrary element of the set (A-B) U (B-A).

So we can conclude that,

(A-B) U (B-A) = (A∪B) - (A∩B)

Hence, proved.