Label each of the following statements as either true or false.
The distinct congruence classes for congruence modulo n form a partition of Z.
The distinct congruence classes for congruence modulo n form a partition of Z.
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
2021-01-17
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sovienesY
Answered 2021-01-18
Author has 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.
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.
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