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Show that this is an equivalence relation , describe
the equivalence set, and state the number of distinct equivalence sets.
Mathematics Homework Solutions
#147744
Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by a ≡ b (mod m) - if a - b is exactly divisible by m, i.e., if a - b is an integral multiple of m. Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.
Topology
Sets and Functions (XLVII)
Functions
Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by a ≡ b (mod m) - if a - b is exactly divisible by m, i.e., if a - b is an integral multiple of m.
Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.
See the attached file.
This solution is comprised of a detailed explanation of the properties of the equivalence relation.
It contains step-by-step explanation of the following problem:
Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by a ≡ b (mod m) - if a – b is exactly divisible by m, i.e., if a – b is an integral multiple of m.
Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.
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