Let A, B, and A_ denote subsets of a space X. Determine whether the following equations hold, if an equality fails, determine whether one of the inclusions or holds.

(1) =

My Work: A B A,B. Thus A B , and therefore A B . Thus

Is this enough? Or do I need further information explaining it, that the part I always lack in my proofs.

(2) = _

My Work: A_ . I only need to show right because I only need to show what inclusion works if equality fails? i'm having the most trouble with this one because i'm very unsure about it.

(3) = - .

My Work: = = - . ...A:=(0,2) B:=(1,2) :=[0,1] - :=[0,1). Is this correct? and/or enough? or again do I need more explanation.

***I am sorry in advanced for my bad latex skills I'm learning and tried very hard this time to make it as clear as I could with what i know.***