Let ≤ be an ordering on a set A. Prove that if ≤ is a well-ordering then it is a linear-ordering.

Question

So i understand that to be an ordering, you have to satisfy the conditions of being reflexive, anti-symmetric, and transitive and for linear-ordering , there should be any a,b such that a ≤ b or b ≤ a but I can't seem to find the connection unless maybe defining some elements to exist in the ordered set.

Answer 1

For any pair $a \neq b$,$\{a,b\}$ must have a minimum.