Prove that:
$(A^{c}\cap B^{c} \cap C) \cup (B \cap C) \cup (A \cap C) = C$
(cmp = complement)
Now, one way to solve this is to take a small universe $U$, say $U$ = {a, b, c, d, e, f, g}, draw the Venn diagram, figure out the union-ed parts of the equation and prove it.
How can we do this purely algebraically? using the laws of sets like the idempotent law, duality, domination, absorption etc?