Quiz 9 Questions - First-Year Interest Group Seminar | N 1, Quizzes of Health sciences

Download Quiz 9 Questions - First-Year Interest Group Seminar | N 1 and more Quizzes Health sciences in PDF only on Docsity! Quiz 9 for M325K Name: UT EID: You may use a calculator otherwise you may give the solutions using factorials. (1) Prove that 1 + 2 + 3 + · · ·+ n = n(n + 1) 2 by induction on n. You may take the base case to be n = 1. (2) Give the 3 properties that a relation R on a set X must satisfy for R to be an equivalence relation. (3) For each of the following functions say whether it is one-to-one, onto, or a bijection. If it is a bijection give a formula for its inverse. (a) f : R → R defined by f(x) = 2x. (b) f : Z → Z defined by f(x) = 2x. (Z means integers) (c) f : Z → {0, 1, 2, 3, 4} defined by f(x) is the remainder after x is divided by 5.