a. Does the definition of A give a binary operation on the set Zt of positive integers, where a Ab=b – 3 is the definition of A? b. Is the binary operation * on the set Zt of positive integers associative, where a * b = a + b is the definition of *? c. Let * be a binary operation on the set {0, 1}, which is defined by the operation table: * 1 0 0 1 10 Is the binary operation * commutative on the set A? Does the binary operation * have an identiy element on the set A? Is the binary operation * an idempotent operation on the set A? ?

a. Does the definition of A give a binary operation on the set Zt of positive integers, where a Ab=b – 3 is the definition of A? b. Is the binary operation * on the set Zt of positive integers associative, where a * b = a + b is the definition of ? c. Let be a binary operation on the set {0, 1}, which is defined by the operation table: * 1 0 0 1 10 Is the binary operation * commutative on the set A? Does the binary operation * have an identiy element on the set A? Is the binary operation * an idempotent operation on the set A? ?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 5E

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