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?