I have the first one as not always true and the second and third as always true. I just wanted someone to check this because I think i'm doing them wrong.Let A,B,C be sets.
(i)Which of the following are always true?
1). A \ ( B \ C) = ( A \ B) U C
2). A \ (B U C) = (A \ B) \ C
3). A \ (B <intersection> C)= (A \ B) U (A \ C)
Is there a difference between A \ B \ C and (A \ B) \ C?
Sorry I don't know how to get unions and intersections to work so I used a U for the union and wrote <intersection> for intersections.
But surely if the set is A not B not C then there would just be A regardless of where you put brackets?I don't think this is a correct writing, unless you can prove (A\B)\C=A\(B\C)
Where did this come from? I'm trying to think of it as a Venn diagram but I can't see what it would look like.
ohhh, so A \ B \ C is not the same as (A \ B) \ C. That seems weird! does "\" mean "not"?
My foundations lecturer introduced "¬" that apparently also means not. It seems strange that he would introduce two different symbols that apparently mean the same thing! (he also did the same for ^ and and it's counterpart with the union. Is there a difference between all this notation???)
Okay then. Going back to the first question:
A \ (B \ C)=A \ (A \ B)
(I used d instead of c since C was already a set).
The second question would become:
Need to show: A \ =(A \ B) \ C
(A \ B) \ C= \ C
Would I need another identity to show that it's true? (if it's true, I think it is). Truthfully, I would much rather remember identities and try to get one side to equal the other side. Venn diagrams are rather limited.