Recent content by marovan

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...