MATH 271 Study Guide - Final Guide: Opata Language, Equivalence Class

• School: University of Calgary
• Department: Mathematics
• Course: MATH 271
• Professor: Thi Ngoc Dinh

Document Summary

The marks for each problem are given to the left of the prob- [8] 1. (a) use the euclidean algorithm to nd gcd(73, 50). Also use the algorithm to nd integers x and y such that gcd(73, 50) = 73x + 50y. 2 (b) use part (a) to nd an inverse a for 50 modulo 73 so that 0 a 72; that is, nd an integer a {0, 1, . , 72} so that 50a 1 (mod 73). Let s be the statement: for all sets a, b, c, if a b and b c = then a c = . (a) prove that s is true. 4 (b) find and simplify the number of two-element subsets s of x that satisfy the following property: a s, ar1. Explain. (c) find the number of subsets s of x (of any size) that satisfy the following property: A s b s so that arb.