Let A and B be finite sets with Suppose (a) If f is one-to-one, show that f is onto B. (b) If f is onto B, prove that f is one-to-one.

▯▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯ ▯▯ ▯▯▯▯▯ ▯ ▯▯▯▯▯ ▯▯▯ ▯▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯ lipeijun@math.purdue.edu ▯ﬃ▯▯ ▯▯▯▯▯▯ ▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯ ▯▯ ▯▯ ▯▯ ▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ www.math.purdue.edu/▯lipeijun/math351.html ▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯ ▯▯▯▯▯▯▯ ▯▯ ▯▯▯▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯▯▯▯▯ ▯▯ ▯▯▯▯▯ ▯▯ ▯ ▯▯▯▯▯ ▯▯ ▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯ ▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯▯▯ ▯▯▯▯ ▯▯▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯ ▯▯ ▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯ ▯▯ ▯▯▯▯▯▯ ▯▯ ▯▯ ▯▯▯ ▯▯▯▯▯▯▯▯▯ ▯▯ ▯▯▯ ▯▯▯▯▯▯ Please staple all pages together. Late h