Mathematics Homework Solutions
#2604
Working with partial order relations in discrete math.
Let S = {0,1} and consider the partial order relation R defined on S X S X S as follows: for all ordered triples (a, b, c) and (d, e, f) in S X S X S.
( a, b, c ) R ( d, e, f ) <-> a ≤ d, b ≤ e, c ≤ f,
where ≤ denotes the usual "less than or equal to" relation for real numbers. Do the maximal, greatest, minimal and least elements exist? If so, which are they?
This shows how to determine if the maximal, greatest, minimal and least elements exist for a given situation.
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