I am a bit confused about a question on proving partial order relation. here is the question and what i done so far.(adsbygoogle = window.adsbygoogle || []).push({});

"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

thanks in advance

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# Partial order relations, on boolean algebra

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