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Let C be the set of cities in the US with populations greater than 200,000 and let L be the relation on C defined by xLy (i.e., (x,y) are members of L) if and only if the population of x is not greater than the population of y. According to one website, |C|=107. Assume, we are looking at the official 2000 census figures
(a) Is the following statement true or false? explain :
There exists an n such that for every x then xLn
(b) Prove or disprove that L is a partial order. There is one sublte issue here; use common sense in dealing with it.