MATH 271 Study Guide - Final Guide: Eulerian Path, Opata Language
12 May 2014
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The marks for each problem are given to the left of the prob- [8] 1. (a) use the euclidean algorithm to nd gcd(77, 62). Also use the algorithm to nd integers x and y such that gcd(77, 62) = 77x + 62y. 2 (b) use part (a) to nd an inverse a for 62 modulo 77 so that 0 a 76; that is, nd an integer a {0, 1, . , 76} so that 62a 1 (mod 77). Let s be the statement: for all positive integers a and b, if a | b then (5a) | (5b). (a) prove that s is true. Let s be the power set p({1, 2, . , 10}); that is, s is the set of all subsets of. De ne the relation r on s by: for all subsets a, b of {1, 2, . 4 (b) find and simplify the number of subsets a {1, 2, 3, .
