# Partial order relations, on boolean algebra

1. Sep 14, 2013

### buchi

I am a bit confused about a question on proving partial order relation. here is the question and what i done so far.

"define the relation '≤' on a boolean algebra B by
for all x,yεB x≤y if and only if xVy=y, show that '≤' is a partial order relation"

first of all what exactly does boolean algebra B look like? can you give me an example of a set A that is a boolean algebra???

I have done alot of examples to prove equivalence relation last week and the idea is straight forward and with this one I first tried to prove reflexivity antisymmetry and transitive

reflexivity:
for any element x that is in B x≤x that is xVx=x???? this part doesnt make sense to me nor do I know what does xVx mean x or x as a set operation 'OR' if so could you guys lead me in a bit

I think once i understand what exactly xVy=y means and how i can manupulate it i think i will be ok to prove antisymmetry transitivity and reflexivity

thanks guys