well-ordered relation help!

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emlevy

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Suppose every nonempty subset of a partially ordered set has a least element. Does it follow that this set is well-ordered? [A well-order relation is a linear order with the property that every non-empty subset S has a least element]
 
Suppose that \(\displaystyle p~\&~q\) are two elements such that \(\displaystyle p \not\prec~\&~q \not\prec p\).
Does the subset \(\displaystyle \{p,q\}\) contain a least term?
 
Suppose the p does not precede q, \(\displaystyle p \not\prec q\), and q does not precede p, \(\displaystyle q \not\prec p\).
In a linear order, given any two elements one precedes the other.

BTW Are your really studying partial ordering and do not know the standard terminology?
 
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