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Give two reasons why the set of odd integers under
Chapter 2, Problem 7E(choose chapter or problem)
QUESTION:
Give two reasons why the set of odd integers under addition is not a group.
Questions & Answers
QUESTION:
Give two reasons why the set of odd integers under addition is not a group.
ANSWER:Step 1 of 2
For a set to be called a Group, the set should follow the rules of Property of Closure, Property of Associativity, Existence of identity and inverse.
According to the Property of Closure over Addition, the sum of two numbers from a set should belong to the set itself.
But in the case of a set of odd numbers, the result of addition is always an even number, which does belong to the set of odd numbers.