Decide whether the given set of numbers is a group under the given operation.
-Whole numbers; addition
A) Yes
B) No

Question

Quizplus · Accepted Answer

For a set to form a group under a certain operation, it must satisfy four properties: closure, associativity, identity, and invertibility. While whole numbers under addition are closed and associative, and have an identity element (0), they lack invertibility. Not every whole number has an additive inverse (a number that can be added to it to yield zero) within the set of whole numbers. For example, there is no whole number that can be added to 1 to get 0, since the additive inverse of 1 is -1, which is not a whole number.

Decide Whether the Given Set of Numbers Is a Group