Let a be the set of all polynomials with real coefficientsa, Ask an Expert

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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.

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