Let f[t] denote the set of all polynomials in the variable t whose coefficients lie in a field f and for which addition and multiplication are defined as in section 1.1. thus, q[t), r[t] and c[t] are the sets of polynomials whose coefficients are, respectively, rational, real and complex (a) show that q[t), r[t], c[t] are integral domains. (b) show that f[t] is an integral domain. (c) interpret z[t) and show that z[t] is an integral domain. (d) interpret f(t1, tm). show that this is an integral domain. we say that f[t] is the set of polynomials over f. 5. (a) show that every field is an integral domain. (b) show that every integral domain satisfies the cancellation law: if ac = bc and c = 0, then a = b. 6. let m > 2 be a positive integer. the set zm consists of the numbers 10.1.2.-1). we define addition and multiplication on this