I'm working some problem in Velleman's How to prove book and is faced with a set in it which goes like this:
$R1 = \{(x,y) \in A \times A \mid \text{the word $y$ occurs at least as late in alphabetical order as the word $x$} \}$
$R2 = \{(x,y) \in A \times A \mid \text{the first letter of the word $y$ occurs at least as late in the alphabet as the first letter of the word $x$}\}$
where $A$ is the set of all words of English.
Can someone give sample set of $R1$ and $R2$ and explain what it means ?
(apple, apple) and (apple,atom) are each in both $R_1$ and $R_2$, but (atom, apple) is only in $R_2$.
In the dictionary, "apple" comes before "atom". This explains $R_1$.
In the alphabet, "a" comes at the same place as "a". This explains $R_2$.