9.11. Summary of Relational Properties 371
Exam Problems
Problem 9.51.
Indicate which of the following relations below are equivalence relations, (E), strict
partial orders (S), weak partial orders (W). For the partial orders, also indicate
whether it islinear(T).
If a relation is none of the above, indicate whether it istransitive(Tr), sym-
metric(Sym), asymmetric(Asym).
(a)The relationaDbC 1 between integers,a,b,(b)The superset relation,on the power set of the integers.(c)The empty relation on the set of rationals.(d)The divides relation on the nonegatitve integers.(e)The divides relation on the integers.(f)The divides relation on the positive powers of 4.(g)The relatively prime relation on the nonnegative integers.The less-than,<, relation on real-valued functions,f.x/, of the formf.x/ D
axCbfor constantsa;b 2 reals.
The relation “has the same prime factors” on the integers.