Text Book: Contemporary Abstract Algebra
Author: Joseph A. Gallien
Edition: 6th
ISBN: 0618514716
Please send solution for below mentions questions
41.) The International Standard Book Numbers (ISBN) a1, a2,a3, a4, a5 , a6, a7,a8,a9,a10 has the property (a1, a2,....................a10) . (10, 9,8, 7, 6, 5, 4, 3, 2, 1) mod 11 = 0. The digits a10 is the check digit. When a10 is required to be 10 to make the dot product 0, the character X is used as the check digit. Verify the check digit for the ISBN assigned to this book
48.) Let S be the set of real numbers. If a,bεS define a
b if a
b is an integer, show that
is an equivalence relation on S. Describe the equivalence classes of S.
49.) Let S be the set of intergers. If a, b ε S, define if ab≥ 0. IS R an equivalence relation on S?
50.) Let S be the set of intergers. If a, b ε S, define aRb if a + b is even. Prove that R is an equivalence relation and determine the equivalence classes of S.
Please send solutions as soon as possible.
Thank you
Hari Putcha