Let A = {a, b, c}. The relation R is defined from A to A as follows R = {(a, b), (a, c), (b, c), (c, a)}.

a) Explain why R is not a function, then find R1 ⊆ R such that R1 is an injective function.

b) Explain why R is not a ”strict” order on A, then find R2 ⊆ R such that R2 is a strict order on A.

c) Explain why R is not an equivalence relation, then show that if R3 is an equivalence relation containing R then R3 = A × A.