Equivalence Relation and Equivalence Sets

Related BrainMass Solutions

• To show that the function f is an equivalence relation

  Define a relation in X as follows: x_1 ~ x_2 means that f(x_1) = f(x_2). Show that this is an equivalence relation and describe the equivalence sets.

• 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 is congruent to 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.

  Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.

• Equivalence Classes of an Equivalence Relation

  This shows that the relation ~ is transitive. Hence the relation ~ is reflexive, symmetric and transitive which imply that the relation ~ is an equivalence relation.

• Equivalence Classes

  the case when n and n' equivalence classes have the relation of subset and superset, i.e., if n>n' => n superset of n' or if n < n' => n subset of n' Hence the maximum number of equivalence sets of p'' = minimum(n,n') --Answer B.)

• Set Theory and Counting

  (a) As the set of even integers and the set of odd integers are disjoint, and the union of these two sets is the set of integers, we conclude that the set of even integers and the set of odd integers form a partition of the set of integers.

• Sets and Binary Relations

  136920 Sets and Binary Relations 2.

• Equivalence and partitions

  If and , then and thus . Hence, the above definition is a well-defined equivalent relation. This shows how to sketch the graph of a given set, prove a set is a partition, and describe the equivalence relation with a given partition.

• Equivalence relations, surjective maps, partitions and fibers.

  123186 Equivalence relations, surjective maps, partitions and fibers. Consider any surjective map f from a set X onto another set Y. We can define a relation on X by x_1 ~ x_2 if f(x_1) = f(x_2). Check that this is an equivalence relation.

• Description of Equivalence Relations

  177043 Description of Equivalence Relations Describe the equivalence relation on each of the following sets with the given partition. (a) Z, {..., {-2}, {-1}, {0}, {1}, {2}. {3, 4, 5, ...}}. (b) R, {(- infinity, 0), {0}, (0, infinity)}.