Jason E. answered • 11/30/21

Professional Math Tutor, 20+ years of experience

a) Yes, of course. Z^{+} X Z^{+} covers all pairs (a,b), where a,b are in Z^{+}

b) Yes. any number in Z^{+} divides itself

c) Yes. If a,b are in Z^{+} , a divides b AND b divides a => a = b

d) Yes. R is total because there is b in Z^{+} for every a in Z^{+}. Namely, a. That is, in plain English, for every positive integer, there exists a positive integer which can be divided by it.

e) Yes. R is a partial order if it is reflexive, antisymmetric, and transitive. R is transitive because if a divides b, and b divides c, a divides c. Again, a,b,c are in Z^{+}

- Jason