- #1

marovan

- 3

- 0

## Homework Statement

$$ A \subset B \Rightarrow A \cap C \subset B \cap C $$

2. Homework Equations [/B]

$$ A \subset B \Leftrightarrow A \cup B \subset B$$

$$ A \cap C \Leftrightarrow A \cap C \subset A \wedge A \cap C \subset C$$

## The Attempt at a Solution

For sets A and C

$$A \cap C \Rightarrow A \cap C \subset A $$

Likewise for sets B and C

$$B \cap C \Rightarrow B \cap C \subset B$$

Therefore

$$A \subset B \Rightarrow A \cap C \subset B \cap C $$

I don't know if I'm completely off the map