Suppose |A| = n, and let F = {f|f is a one-to-one, onto function from I, to A}. Prove that F is finite, and |F | = n!. (Hint: Use induction on n.) Let L = {R| R is a total order on A}. Prove that F =...

Extracted text: Suppose |A| = n, and let F = {f|f is a one-to-one, onto function from I, to A}. Prove that F is finite, and |F | = n!. (Hint: Use induction on n.) Let L = {R| R is a total order on A}. Prove that F = n!. Five people are to sit in a row of five seats. In how many ways can they be seated? L, and therefore |L|