Chains of people names 
Consider the set $X$ of possible names for people. Let $(x, y) \in P$
  (in the partial order) if and only if $x$ ends in a consonant and $y$
  ends in a vowel. What is the length of the longest chain here? Give a
  total order of the elements in $X$.

I don't really get how it is a binary relation and how to approach this problem.

I believe you are to consider the names in $X$ to be single words, not a first name/last name pair.  Hint:  if a name ends in a consonant it can only be the first element of a pair, while if it ends in a vowel it can only be the second element of a pair.  How long a chain can you make?  I think the last sentence is a completely separate question-you are just asked to define a new relation that is a total order.
