Question

R be a relation in a set A. Then R is an equivalence relation in A if and only if _____________________________.

• A. R is reflexive, R is symmetric and R is transitive
• B. R is antireflexive, R is symmetric and R is transitive
• C. R is antireflexive, R is antisymmetric and R is transitive
• D. None of the above

Answer 1

The correct option is A R is reflexive, R is symmetric and R is transitive

R is a relation in a set a. then R is an equivalence relation in A if and only if R is reflexive, R is symmetric and R is transitive.

Equivalence relation:-

An equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation, where for any objects a, b, and c.

Reflexive relation:-

A reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself.

Transitive relation:-

A binary relation Rover a set Xis transitive if whenever an element ais related to an element band bis related to an element cthen ais also related to c. Transitivity is a key property of both partial order relations and equivalence relations.

Symmetric relation:-

A binary relation R over a set X is symmetric if it holds for all a and b in X that a is related to b if and only if b is related to a.