How do I prove that (A△B)∩C = (A∩C)△(B∩ C)? And I can't seem to draw the Venn diagrams how would A∩C look?

Question

anonymous · Answer

we can prove this in two ways either be by using venn diagram or algebraically. Venn diagram would be easier I believe .. 

btw do you understand what is $$  A△B $$ means ?

anonymous · Answer

Yeah elements of A and B but not both

anonymous · Answer

for the A∩C would it  be only A and C

anonymous · Answer

|dw:1322079566158:dw|

anonymous · Answer

so like that?

anonymous · Answer

it is  known as symmetric difference and symbolically represented as  $$A  \Delta  B$$ and  $$ A \ominus B $$

anonymous · Answer

picture is like this http://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/200px-Venn0110.svg.png

anonymous · Answer

I think your representation of (A△B)∩C is not correct

anonymous · Answer

no that's for A∩C

anonymous · Answer

as you are including some parts of A∩B which is not intended. Did you get it ?

anonymous · Answer

okay let me draw out what I think is right

anonymous · Answer

oh sorry .. yes that's correct then..

anonymous · Answer

okay so what do you want now ? :)

anonymous · Answer

the first part I don't see how they are equal.. (A△B)∩C = (A∩C)△(B∩ C)

anonymous · Answer

with the venn b/c I got two different venns

anonymous · Answer

|dw:1322079944185:dw| this is for (A∩C)△(B∩ C)