# Midterm Practice: Could some verify my proof

1. May 28, 2005

### johnnyICON

Midterm Practice: Could someone verify my proof

A sample question that I tried proving is:

Formally show that $$A \subseteq B,~then~A \cap C \subseteq B \cap C$$

My Proof:
Suppose $$x \in A \cap C$$. Then by definition of intersection, $$x \in A~and~x \in C$$. But as $$A \subseteq B,~then~x \in B$$. Hence, $$x \in B \cap C$$. And therefore, $$A \cap C \subseteq B \cap C$$.

Is there anything that I've missed? Is this even right?

Last edited: May 28, 2005
2. May 28, 2005

### mathman

It looks fine to me.

3. May 28, 2005

Hallelujah!