Mathematics II20805 marksGroups
Define group. Show that the set of integers is a group with respect to addition operation.
Define group. Show that the set of integers is a group with respect to addition operation. [5]
Definition: A non-empty set G together with a binary operation \ is called a group, denoted (G, ), if the following axioms are satisfied: 1. Closure: For all a, b ∈ G, a \ b ∈ G 2. Associativity: For all a, b, c ∈ G, (a \ b) \ c = a \ (b \ c) 3. Identity: There exists an element e ∈ G such that ...