Question

Find one counter example to the following incorrect theorem.

Suppose F and G are families of set. If ∪F and ∪G are disjoint, then F and G are also disjoint.

Answer 1

suppose they are both empty?

Answer 2

If F and G are both empty then ∪F and ∪G are disjoint and F and G are also disjoint. But this isn't a counter example

Answer 3

So wait, the empty set and the empty set are disjoint? And their intersection is the empty set? Hurts my brain

Answer 4

yeah that's why the empty set is a very special set. Just like the number 1 when it comes to prime numbers