# 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

That means

if

if

Thus

We have proven that

2.- Let

That means

So

That means

Thus we have

We have proven that

Both inclusions are true, so

QED (Quod Erat Demonstrandum in Latin)