if and only if .
Does that work?
P.S. Here is another ‘fun’ one for symmetric difference.
.
I just wanted to make sure my proofs are correct.
Given the indicator function.
show that:
i) :
Proof:
which implies that
ii)
Proof:
now can be written as two disjoint sets so we have
so we have :
where the terms are expanded out.
iii)
I have no idea