Chapter 9.3, Problem 10E

many nonzero entries does the matrix representing the relationRonA={1, 2,3,..., 1000} consisting of the first 1000 positive integers have ifRis

a) $\left\{\left(a,b\right)|a\le b\right\}$?

b) $\left\{\left(a,b\right)|a=b\pm 1\right\}$?

c) $\left\{\left(a,b\right)|a+b=1000\right\}$?

d) $\left\{\left(a,b\right)|a+b\le 1000\right\}$?

e) $\left\{\left(a,b\right)|a\ne 0\right\}$?