Question

Prove A-(A-B)=B-(B-A)

Answer 1

For Set theory

Answer 2

Of course I need to show forward and converse. I also started the forward with "Let be x within A-(A-B)."

Answer 3

not sure where to go from there...

Answer 4

So by definition, x is in A, but x is not in A-B. So x must be in B as well. Now since x is in A, x is not in B-A. Hence x is in B-(B-A).

Now go the other way!

Answer 5

hmm that was quite simple. *face palm*

Answer 6

Thanks

Answer 7

@Erin001001 Thanks!

Answer 8

No problem :) What you really needed was a picture: with a Venn diagram and a bit of shading, it should be fairly easy to show that is x is in the LHS it must be in \(A \cap B\).

Answer 9

I started with a Venn diagram and then got to the proof and couldn't see how to relate the two expressions.