check the working ( set )

[denian]

using algebraic laws of sets, show that, for any set A and set B that

( A U B ) [inter] ( A U B' ) = A


this is my working

( A U B ) [inter] ( A U B' )

= A U ( B [inter] A ) U ( B [inter] B' )

= ( A U B ) [inter] ( A U A )

= ( A U B ) [inter] A

= A U ( B [inter] A )

= A ( shown )


i think this working is wrong. is there other way better than this?

[arcnets]

denian,
I think the 1st step should be

( A U B ) [inter] ( A U B' )

= A[inter]A U A[inter]B' U B[inter]A U B[inter]B'

[denian]

ok. i dont even know we can expand it that way.
thank you.