- #1

- 103

- 4

## Homework Statement

##C \subseteq A \cap B \implies A \cap B \cap C = C##

## Homework Equations

How do I get rid of the "belongs to" term on the right hand side? I know I need to prove either the left hand or the right hand side of the "or" term is correct, I'm just not sure how to get there.

## The Attempt at a Solution

~##(C \subseteq A \cap B) \cup (A \cap B \cap C = C)##

__right hand side (right of the "or"):__

##C \subseteq A \cap B \cap C## (Trivial)

##A \cap B \cap C \subseteq C## (This is the one we want to prove)

So all together:

~##(C \subseteq A \cap B) \cup (A \cap B \cap C \subseteq C)##

##\exists x \in C \therefore x \in A \cap B)##

##(\sim a \cup \sim b) \cup (a \cap b \cap c \subseteq C)##