what are examples of equivelence relations?

Question

please give numerical examples

Answer 1

A relation R on a set S is an equivalence relation on S if and only if R is
(a) reflexive, that is, x R x for all x in S,
(b) symmetric, i.e., if x R y, then y R x for all x, y in S, and
(c) transitive, i.e., if x R y and y R z, then x R z for all x, y, z in S.

Equality (R) on the set (S) of reals is the best known example of an equivalence relation.

Another example is congruence on the set of integers: we say a is congruent to b modulo m if and only if m divides b - a. For example 4 is congruent to 7 modulo 3 because 3 divides 4 - 7. You should be able to prove that congruence is reflexive, symmetric, and transitive.

Answer 2

An equivalence relation is a relation between two elements of a set such that the relationship is reflexive, symmetric, and transitive.

If A is the set of real numbers, the relation "addition" of two numbers is reflexive, symmetric, and transitive, so this is an equivalence relation .

If A is the set real numbers, the relation "subtraction" of two numbers is not symmetric (x-y does not equal y-x), so this is not an equivalence relation.

Answer 3

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Answer 4

I don't know if this is what you need

x = 2 . . . . 2 and x are equivalent or equal
tan x = 1/ cot x . . . . . identities are also equivalence
2.2. lbs = 1 Kg . . . . . in unit measure
1 cu. ft. = 7.48 gallons . . . . equivalence of volume
1 minute = 60 sec . . . . . time unit has also equivalence
5 ft. 7 inches = 170 cm . . this is my height in different units
E = mc^2 . . . . . this is the equivalence of energy to matter
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thanks for the light of wisdom , . . it shines equally to all men