So I pretty much have had decent success in this entire Module I've been working on but proving counterexamples are still stumping me for some reason. I did a 120 question homework assignment and there's two questions I cannot figure out. Maybe somebody can assist me:
Let A, B, and C be sets. (a.) Find a counterexample to the statement A union(B intersects C)=(A union B)intersects C.
(b.) Without using a Venn diagram, prove that: A union(B intersects C)=(A union B)intersects(A union C)
I tried pasting the symbols for union and intersect but they came up as "?" when I previewed the post. Now for some reason I get very confused when it comes time to creating a proof and a counterexample. I'll attach the assignment as well just in case you would like to see everything I'm working on in addition to my answers. If somebody can help me understand this better I would really appreciate it. Thank you.