Problem of the Day

Chapter 1, Lesson 9

Consider this set of numbers: {0, 1, 2, 3, 4}.
Add the elements of this set using this rule:
Add normally; but if the sum is more than 4, subtract 4.
To show that this is not usual addition, use the symbol ?.
Examples: and
Find all the possible sums and organize the results in this table.
The results of the examples are already in the table.

Is this set of numbers closed under the operation
Justify your answer.