Textbook Problem

(a) How many even integer are in the set $\left\{1,2,3,\mathrm{...},100\right\}?$

(b) How many odd integers are in the set $\left\{1,2,3,\mathrm{...},100\right\}?$

(c) How many ways can two integers be selected from the set $\left\{1,2,3,\mathrm{...},100\right\}$ so that their sum is even?

(d) How many ways can two integers be selected from the set $\left\{1,2,3,\mathrm{...},100\right\}$ so that their sum is odd?