Label each of the following statements as either true or false. The distinct congruence classes for congruence modulo n form a partition of Z.

amanf

amanf

Answered question

2021-01-17

Label each of the following statements as either true or false.
The distinct congruence classes for congruence modulo n form a partition of Z.

Answer & Explanation

sovienesY

sovienesY

Skilled2021-01-18Added 89 answers

Consider the statement, “The distinct congruence classes for congruence modulo n form a partition of ZZ”.
By using the theorem,
The relation of congruence modulo n is equivalence relation on Z.
As with any equivalence relation, the equivalence classes for congruence modulo n form a partition of ZZ, that is, they separate ZZ into mutually disjoint subsets.These are called congruence classes or residue classes.
Hence, the statement, “The distinct congruence classes for congruence modulo n form a partition of ZZ” is true.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?