Prove or disprove for all sets A, B and C that (A − B) − C = (A − C) − B

Answer 1

PROOF

Recall that if X and ϒ are sets X− Y = X ∩ ϒ^c ( Difference Law )

[ A− B ] − C = [ A ∩ B^c ] ∩ C^c by Difference Law

= A ∩ [ B^c ∩ C^c ] By Associative Law

= A ∩ [ C^c ∩ B^c ] by Commutative Law

= [ A ∩ C^c ] ∩ B^c By Associative Law

= [ A− C ] − B by Difference Law