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?
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?
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