Ok so over the summer I decided to read Apostol's Calculus Vol. 1 and my only background in calculus is in a high school calculus class, so I know the extreme basics and am trying to put my knowledge on a my rigorous footing.(adsbygoogle = window.adsbygoogle || []).push({});

I think my biggest problem is definitely writing my own proofs. I just started so I'm still in the section that covers basic set theory and it asks to prove commutative and associative properties involving unions and intersections. I think I can prove the commutative law but the associative law is proving (pun intended) to be quite difficult for me. I just seem to be going around in circles just writing out the problem so I was wondering if anyone could critique this bad attempt and give me some sort of starting place.

Prove [tex](A \cup B) \cup C = A (B \cup C)[/tex]

Let [tex]x \in A, y \in B, z \in C[/tex] and let [tex]D = A \cup B, E B \cup C[/tex]

This implies D = {x, y} and E = {y, z}

So [tex]D \cup C =[/tex] {x, y, z} and [tex] A \cup E =[/tex] {x, y, z}

Therefore [tex]D \cup C = A \cup E = (A \cup B) \cup C = A (B \cup C)[/tex]

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# Help with proof

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