All right
$$ A \subset B \Leftrightarrow (x \in A \Rightarrow x \in B) $$
As for A∩C⊂A
$$ A \cap C \Leftrightarrow (x \in A and x \in C) $$
$$ If x \in C then x \in A \cap C \Leftrightarrow x \in A $$
Therefore, since A ∩ C ⊂ A and likewise for B ∩ C then A ∩ C ⊂ B ∩ C
I'm sorry..
I have to proof the first statement.
I have attempted at a proof, but I don't know if it's the right way to do so. I'm asking for a little guidance
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...