Question

Prove that (A-B) union (B-A) = (A union B)-(A intersection B)

Answer 1

Answer:

Use definition:

• A - B = A ∩ B'    [ here using ' to indicate complement ]

Then

( A - B ) ∪ ( B - A )

= ( A ∩ B' ) ∪ ( B ∩ A' )

= ( A ∪ B ) ∩ ( A ∪ A' ) ∩ ( B' ∪ B ) ∩ ( B' ∪ A' )

= ( A ∪ B ) ∩ ( B' ∪ A' )

= ( A ∪ B ) ∩ ( A ∩ B )'      [ De Morgan's Law ]

= ( A ∪ B ) - ( A ∩ B )