I'm not able to understand the folowing example from Dirk van Dalen's logic and structure. What is confusing me is the relation defined on the structure and the predicate $P $.

[![enter image description here](https://i.stack.imgur.com/f9Go7.jpg)](https://i.stack.imgur.com/f9Go7.jpg)

We have a set $A=\{0,1 \} $ and a relation defined on $A $ as the set with two elements $\{\langle 0.1 \rangle , \langle 1,0 \rangle \}$. I'm not sure what to make of this relation (being used to relations such as $<, = $ etc on say $\mathbb N $) . (Maybe the elements should just be thougt of as saying, $0 $ is in relation with $1 $ and $1 $ is in relation with $0 $.)

Then I'm not sure of how the predicate $\phi := P(x,y) $ is defined. (But he speaks of $\langle 0,1 \rangle $ being an element of $P $ and thus it should be thought of as a set?)