Help with some set theory questions

[Beno]

Greetings all. I was wondering if someone could give me some asistance on a few simple set theory proofs.

1) An(B\C)=(AnB)\(AnC)
2) A+(B+C)=(A+B)+C where + = symmetric difference
3) If A+B = A+C then B=C
and
4) An(B+C) = (AnB)+(AnC)

 

[tiny-tim]

Welcome to PF!

Hi Beno! Greetings and welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Beno]

With number 1
An(B\C)=(AnB)\(AnC)
I tried the following
An(B\C) = An(BnC') =(AnB)n(AnC') but this was as far as it seemed to go.

As for the others I think I've worked them out since posting

 

[tiny-tim]

With number 1
An(B\C)=(AnB)\(AnC)
I tried the following
An(B\C) = An(BnC') =(AnB)n(AnC') but this was as far as it seemed to go.

ok, let's do some reverse engineering …

the last step but one is going to be (AnB)n(AnC)' …

work backwards from there. ​