Question

Let R={(x, x0 (y, y)(2, 2)(x, z)}. What are the properties
of equivalence relation satisfied .​

Answer 1

Answer:

A relation R on a set A is said to be an equivalence relation if and only if the relation R is reflexive, symmetric and transitive.

Reflexive: A relation is said to be reflexive, if (a, a) ∈ R, for every a ∈ A.

Symmetric: A relation is said to be symmetric, if (a, b) ∈ R, then (b, a) ∈ R.

Transitive: A relation is said to be transitive if (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.

Equivalence relations can be explained in terms of the following examples:

• The sign of ‘is equal to (=)’ on a set of numbers; for example, 1/3 = 3/9.
• For a given set of triangles, the relation of ‘is similar to (~)’ and ‘is congruent to (≅)’ shows equivalence.
• For a given set of integers, the relation of ‘congruence modulo n (≡)’ shows equivalence.
• The image and domain are the same under a function, shows the relation of equivalence.
• For a set of all angles, ‘has the same cosine’.
• For a set of all real numbers,’ has the same absolute value’.