Let F be a field, and p(x) E F[x] an irreducible polynomial of degree od. Prove that every coset of Flr]/(p) can be represented by a unique polyno- mial of degree strictly less than d, and moreover that these are all distinct. Prove that if F has q elements, F[x]/(p) has q elements. has ql elements.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.