Exercise 4.1 Give an example of a relation that is neither strict nor reflexive.
Consider the relation defined on integers where r(a, b) if and only if a + b is divisible by 4. Then r is not strict (since r(2, 2) holds), but r is not reflexive (since r(3, 3) does not hold).
Alternatively, consider the relation defined on positive integers where r(a, b) if and only if the sum of the proper (positive) divisors of a is equal to b. Then r(6, 6) holds, since 6 = 1 + 2 + 3, but r(7, 7) does not hold, since 7 != 1. Note that by definition, r(a, a) if and only if r is a "perfect number".