Which of the following are equivalent relations?

Question

equalities and congruence are examples of relations. a relation that is reflexive, symmetric, and transitive is the equivalence relation. which of the following are equivalent relations??

a- >
b- is the brother of
c- ≠
d- is a complement of

Answer 1

That should be equivalence relation not equivalent.

A relation must be defined on a set. You don't give any sets.
Although you can make assumptions for them I suppose.

a. Assume the set is the real numbers. Then this relation is not reflexive. A number can't be greater than itself.

b. Assume some set of people. Since a person can't be their own brother, this is not reflexive either.

c. Assume some set of numbers. This will not be reflexive either. A number will never not equal itself.

d. Assume the set of all angles. Yet again, it isn't reflexive. An angle of one degree is not the complement of itself.