Element Proof of (A∩B)^c=A^c ∪ B^c

Question

For all sets A and B, (A∩B)^c=A^c∪B^c

Answer 1

This is known as DeMorgan's Rule

Proof:

x is an element of complement((A intersect B))

Then x is NOT in A intersect B, which means x is NOT in the intersection of A and B.

So then either x is not in A or x is not in B

if x is not in A then x is in complement(A)

if x is not in B then x is in complement(B)

so x is either complement which completes the proof