What is the composition of the relation | (divides) and ?
My general interpretation:
Let be the | relation, and be . should be the set of all points where divides some .
If this is correct, (I'm not sure) how would I express this as set-builder notation?
?
Hmm.. My book states the following regarding a composition:
From that definition, I do not see why the composition of | and should be given and as previously.Given relations and , the composition consists of all pairs for which there is a with and .
Perhaps I missed something?
Think of function composition. Suppose that .
In the composition ‘do the function’ first then we ‘do the function’:
we first add one then square the result .
On the other hand reverses the order: we first square it and add one to the result .
That also true of relations. The order is from right to left.
So doing the divisor first and then the less than or equal to, we get .