# Math Help - Venn Diagram proof?

1. ## Venn Diagram proof?

Proof for all sets A, B, and C:
A complement Union B complement = (A Intercept B) complement.

can someone help??

2. Note: to show that two set are equal we need to show

$(A^c \cup B^c) \subset (A \cap B)^c$ and $(A \cap B)^c \subset (A^c \cup B^c)$

let $x \in (A^c \cup B^c)$ by definition

$x \in A^c \mbox{ or } x \in B^c$ by negation

$x \notin A \mbox{ and } x \notin B$ by definition

$x \notin (A \cap B)$ (def of compliment) Since x is not in A and B it must be in

$x \in (A \cap B)^c$

This is half the proof Now you need to show the 2nd part.

Good luck

P.s. I think this is one form of DeMorgans Law.