I am doing a text that my big brother gave me: Mathematical Analysis I - Zorich. This stuff is pretty hard for me, since in class we don't do sets.
I can see why they are true with pictures, but i don't know how to prove them mathematically:
1.a) $(A \subset C) \wedge (B \subset C) \Leftrightarrow ((A \cup B) \subset C)$
I can see that if the left is true, the right is true, and if one is false, the other is false.
but what if $A$ exclusively OR $B$ subsets C, then the right is true, but the left is false?
1.b) $(C\subset A) \wedge (C \subset B) \Leftrightarrow (C\subset (A \cap B))$
This seems obvious, but how to mathematically show it? i can just draw the Venn diagram again, but that is not math?
Side question: Do Venn diagrams count as mathematical proofs? Or are they just a tool to clear things up?