Chapter 1.3, Problem 12E

Suppose the polynomials $a_n{x}^n+a_{n-\text{1}}{x}^{n-\text{1}}+...+a_0$ and $b_n{x}^n+b_{n-\text{1}}{x}^{n-\text{1}}+...+b_0$ are not equal. Which of the following must be true?
(a) $a_n\ne b_n$ .
(b) $a_i\ne b_i$ whenever $0\le i\le n$ .
(c) $a_i\ne b_i$ for every isuch that $0\le i\le n$ .
(d) $a_i\ne b_i$ for some isuch that $0\le i\le n$ .
(e) It is not the case that $a_i=b_i$ for all isuch that $0\le i\le n$ .
(f )It is not the case that $a_i=b_i$ for some isuch that $0\le i\le n$ .
(g) There is an isuch that $0\le i\le n$ and $a_i\ne b_i$ .
(h) If $a_i=b_i$ for all isuch that $0\le i\le n-\text{1}$ , then $a_n\ne b_n$ .