Cardinality - Discrete Math - Quiz, Exercises of Discrete Mathematics

Download Cardinality - Discrete Math - Quiz and more Exercises Discrete Mathematics in PDF only on Docsity! Prof. S. Brick Math 267 Fall ’03 Discrete Math; Final section 101 Print your name: Directions: Show all of your work, and explain your reasoning. 1. Prove by induction that a finite set of cardinality n has 2n subsets. 2. Find the transitive closure of the relation {(a, 7), (7, y), (y, x), (7, 12)}. 3. Give a combinatorial proof of C(n + 1, k + 1) = C(n, k) + C(n, k + 1). (A proof which involves formulas or algebra is not worth any points here.) 4. Find the generating function of the recurrence relation given by “a0 = 2, a1 = 1 and an = 3an−1 − an−2 for n ≥ 2”. The first 4 terms followed by a “+ . . .” suffices.