Let A be the set of all polynomials with real coefficients.
a. Assume R is the relation such that fRg if and only if deg(f) = deg(g). Is this an equivalence relation? If so, prove it. If not, explain why.
b. Suppose R = {(f,g) : f(c) = g(c) for some c}. Is this an equivalence relation? If so, prove it. If not, explain why.