1. Three dice, 1, 2, and 3, are rolled independently. • Event A12 is that dice 1 and 2 show the same number. • Event A13 is that dice 1 and 3 show the same number. • Event A23 is that dice 2 and 3 show the same number. (a) Are events A12 and A13 independent? (b) Are the three events independent?
5. (Sudden death) The NHL has another season-long strike, but the owners and players reach an agreement in June which leaves time for a highly abbreviated season. They decide that fans want to see the Stanley Cup decided, and so they play only a sudden-death version of the seventh game of the final round of the playoffs. Her ...continues
(See attached file for full problem description) --- Proposition 10.2.1: (the addition principle) Suppose that X and Y are disjoint finite sets. Then X U Y is finite and |X UY| = |X| + |Y|. Corollary 10.2.2: For a positive integer n, suppose that X1, X2….,Xn is a collection of n pairwise disjoint finite sets (i.e. i ...continues
Need help in determinimg proof for the following.
Need help in deciphering proof for the following. (See attached file for full problem description)
Need help in determining the following proof. (See attached file for full problem description) --- Thm 11.1.2 (the pigeonhole principle): Suppose that f:X Y is a function between non-empty finite sets such that |X| > |Y|. Then f is not an injection, i.e. there exist distinct elements x1 and x2 E (epsilon) X ...continues
Need help in determining the following proof exercises. Please use general logic notation such as U. (See attached file for full problem description) --- Proposition 10.2.1: (the addition principle) Suppose that X and Y are disjoint finite sets. Then X U Y is finite and |X UY| = |X| + |Y|. Corollary 10.2.2: Fo ...continues
Number Theory. 400 level. Introductory Course in Undergraduate.
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields. (See attached file for full problem description)
Number Theory. 400 level. Introductory Course in Undergraduate.
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields. (See attached file for full problem description)
Number Theory. 400 level. Introductory Course in Undergraduate.
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields. (See attached file for full problem description)
