Does this proof work?

[demon8991]

(A union B) intersection (A union C) = A union (B intersection C)

I have go an eqaution and i want to proove that it works, is this correct?

Choose an aribitary X belongs to (A union B) intersection (A union C), then X belongs to A union B and X belongs to A union C.

If X doesnt belong to A then X must belong to B and C which means that X belongs to B intersection C.

Which means X belongs to A union (B intersection C) this remains true when X belongs to A.

Therefore X belongs to (A union B) intersection (A union C) implies that X belongs to A union (B intersection C) and becuase X is arbitary this is trye for every such X and so.

(A union B) intersection (A union C) is a subset of A union (B intersection C)

Doing very much the same thing you can then prove that:

A union (B intersection C) is a subset of (A union B) intersection (A union C)

And becuase they are both subsets of each other then.

(A union B) intersection (A union C) = A union (B intersection C)

is correct?

Please tell me this is right...

 

[demon8991]

Ahhh brilliant im glad that it works.

Yer i was going to do that just thought people may get confused for it being another variable.

 

[demon8991]

Out of interest does this work the exact same way for.

(A intersection B) union (A intersection C) = A intersection (B union C)

 

[demon8991]

Wicked so the proof is identical just with the opposite notation?

 

[demon8991]

Brunel

 

[demon8991]

Yer im doing it as part of my university course, finding parts of it quite confusing as its unlike any maths ive done before its much more abstract.