Proof for all sets A, B, and C:
A complement Union B complement = (A Intercept B) complement.
can someone help??
Note: to show that two set are equal we need to show
$\displaystyle (A^c \cup B^c) \subset (A \cap B)^c$ and $\displaystyle (A \cap B)^c \subset (A^c \cup B^c) $
let $\displaystyle x \in (A^c \cup B^c) $ by definition
$\displaystyle x \in A^c \mbox{ or } x \in B^c $ by negation
$\displaystyle x \notin A \mbox{ and } x \notin B $ by definition
$\displaystyle x \notin (A \cap B)$ (def of compliment) Since x is not in A and B it must be in
$\displaystyle x \in (A \cap B)^c$
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.