Sort of difficult to see what you want to prove like this...
Did you mean: ?
My teatcher wasn't able to explain this for me in a clear way. See if you guys can help.
Let A and B be two random sets. Prove that A \times" alt="\times" /> B (B \cap" alt="\cap" /> C) = (A \times" alt="\times" /> B) \cap" alt="\cap" /> (A \cap" alt="\cap" /> C) by putting in the element (x,y)
Ok, this is how the question looks like and what the key says.
Let (x,y) be a random element in
Then we have that X A and y B C which give y B and y C.
(x,y) A x B and (x,y) A x C so (x,y) (A x B) (A x C)
and now we can prove that (A x B) (A x C) A x (B C).
But I don't get a grip over this. For example why do you have to put the x in A and the y in (B C) and not the other way around?
I would like to see this in a graphic 3D model so I could see what I was doing.