Chapter 9.1, Problem 43E

R₁andR₂be the “congruent modulo 3” and the “congruent modulo 4” relations, respectively, on the set of integers. That is, $R_1=\left\{\left(a,b\right)|a\equiv b\left(\mathrm{mod}3\right)\right\}$and $R_2=\left\{\left(a,b\right)|a\equiv b\left(\mathrm{mod}4\right)\right\}$. Find

a) $R_1\cup R_2$.

b) $R_1\cap R_2$.

c) $R_1-R_2$.

d) $R_2-R_1$.

e) $R_1\oplus R_2$.