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## Homework Statement

Are the following subsets partitions of the set of integers?

The set of integers divisible by 4, the set of integers equivalent to 1 mod 4, 2 mod 4, and 3 mod 4.

## Homework Equations

## The Attempt at a Solution

Yes, it is a partition of the set of integers. Consider 4/4 = 1, 5/4 = 1 R 1, 6/4 = 1 R 2, 7/4 = 1 R 3.

However, how would you create a negative number like -5?