The following relations are all equivalence relations: "Is equal to" on the set of numbers. For example, is equal to "Has the same birthday as" on the set of all people. "Is similar to" on the set of all triangles. "Is congruent to" on the set of all triangles. Given a natural number , "is congruent to, modulo " on the integers. Given a function , "has the same image under as" on the elements of 's domain . For example, and have the same image under , viz. . "Has the same absolute value as" on the set of real numbers "Has the same cosine as" on the set of all angles.
The following relations are all equivalence relations "Is equal to" on the set of numbers. For example, is equal to "Has the same birthday as" on the set of all people. "Is similar to" on the se,t of all triangles. "Is congruent to" on the set of all triangles. Given a natural number  "is congruent to, modulo " on the integers. Given a function , "has the same image under as" on the elements of 's do:main . For example, and have the same image under  viz. . "Has the same absolute value as" on the set of real numbers ,"Has the same cosine as" on the set of all angles.