Rosen , Ch-9, Ex-1, Que. 41

Question

Let R1 and R2 be the “congruent modulo 3” and the
“congruent modulo 4” relations, respectively, on the set
of integers. That is, R1 = {(a, b) | a ≡ b (mod 3)} and
R2 = {(a, b) | a ≡ b (mod 4)}. Find

a) R1 ∪ R2.
b) R1 ∩ R2.
c) R1 − R2. 
d) R2 − R1.
e) R1 ⊕ R2.

Can someone explain the logic?

Answer 1

try this using theory of computation. finite state machines.