Thread: Partial Order - maximum minimum and maximal

Let

R be a partial order relation on a set A.
Prove that if x belonging toA is a maximum then it is maximal.
Prove that if x belonging to A is a minimum and a maximum then A={x}.

someone can help me???

Those look like they should be easy if you know the definitions.

What is the difference betweeen a "partially ordered set" and a "linearly ordered set"? What is the difference between "maximal" and "maximum". And, most importantly, what do "maximum" and "minimum" mean?