How do you prove this? 7) For sets A,B,C prove (A - B) ∪ (C - B) = (A ∪ C) - B by showing Left side ⊆ Right side and Right side ⊆ Left side.

1 Answer
Jan 31, 2018

The proposition is true

Explanation:

1.- Let x(AB)(CB)
That means x(AB)orx(CB)
if x(AB) that means xA and xB
if x(CB) that means xC and xB
Thus x(AC)B
We have proven that (AB)(CB)(AC)B
2.- Let x(AC)B
That means xAC but xB
So xA or xC but in both cases xB
That means xAB or x(CB)
Thus we have x(AB)(CB)
We have proven that (AC)B(AB)(CB)
Both inclusions are true, so
(AB)(CB)(AC)B
QED (Quod Erat Demonstrandum in Latin)