Symmetric Difference Explanation

[gutnedawg]

Can someone explain to me how to show (x\y) union (y\x) = (x union y) \ (y union x) using only the main set theory laws for union, intersections and difference.

 

[micromass]

I have a feeling that this is a homework problem, so I'm not going to tell you a lot.

How do you usually show the equality of sets?

 

[tiny-tim]

hi gutnedawg!

shouldn't that be (x union y) \ (x intersection y) ?

anyway, start by writing x\y in terms of unions or intersections …

what do you get? ​

 

[gutnedawg]

hi gutnedawg!

shouldn't that be (x union y) \ (x intersection y) ?

anyway, start by writing x\y in terms of unions or intersections …

what do you get? ​

yea sorry I meant to write union and then intersection not union and union

this is not a homework problem this problem was posted in lecture for us to try on our own and I'm having trouble starting it

EDIT how could I write x\y in terms of intersections and unions... The professor suggested using the absorption laws but I'm not sure how to go on from rewriting x and y with the absorption laws

 

[verty]

You've just got to apply the laws in different orders until you find the order that works. Trial and error, I'm afraid.

 

[gutnedawg]

You've just got to apply the laws in different orders until you find the order that works. Trial and error, I'm afraid.

care to give any hints?

 

[tiny-tim]

hi gutnedawg!

(just got up :zzz: …)

EDIT how could I write x\y in terms of intersections and unions... The professor suggested using the absorption laws but I'm not sure how to go on from rewriting x and y with the absorption laws

(what are the absorption laws? )

x\y = x intersection not-y ​

 

[jambaugh]

General advice,
Set operations exactly mirror first order logic. Translate any set to the statement that some antecedent object is in the set. X --> "p is in X".

Then you can use your verbal skills to parse set operations...

x\y -> " p is in x and not in y".

A Venn diagram is also quite useful. Between Venn diagrams and translation to logic you can utilize your visual and verbal skills to better understand the set operations.

Finally ask yourself why your Professor didn't just tell you the answer and then trust his judgment. (Hint, you can't learn to swing a golf club by just watching the Pro's.)