In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?
A. an element n exists for which m=n
B. An element m is maximal in the poset
C. A set with the same subset of the poset
D. An element m is minimal in the poset
Answer:B
In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?
A. an element n exists for which m=n B. An element m is maximal in the poset C. A set with the same subset of the poset D. An element m is minimal in the poset
Explanation: By the definition, an element m exists in a poset (S, ⪯) is maximal if and only if there is no n∈S with m≺n.