Question

Answer for (A-B)U(B-A) in sets

Answer 1

The answer is AUB
A-B=A
B-A=B
(A-B) U (B-A)=AUB
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Answer 2

Answer:

(A-B) ∪ (B-A) = (A ∪ B) - (A ∩ B)

Step-by-step explanation:

Let U be the universal set.

Step 1:

We know that the difference between two sets is equal to the intersection of the first set with the complement of the second set.

(A-B) ∪ (B-A)

⇒ (A ∩ B') ∪ (B ∩ A')

Step 2:

Using the distributive property of ∪ over ∩.

⇒ { (A ∩ B') ∪ B } ∩ { (A ∩ B') ∪ A'}

⇒ { (A ∪ B) ∩ (B' ∪ B) } ∩ { (A ∪ A') ∩ (B' ∪ A') }

The union of a set with it complement set gives back the universal set U.

⇒ { (A ∪ B) ∩ U } ∩ { U ∩ (B' ∪ A') }

Step 3:

The intersection of any set with the universal set is the set itself.

⇒ (A ∪ B) ∩ (A ∩ B)'

The difference between two sets is equal to the intersection of the first set with the complement of the second set.

⇒ (A ∪ B) - (A ∩ B)

Therefore, the answer for (A-B) ∪ (B-A) in sets is (A ∪ B) - (A ∩ B).

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