Question

let the relation on the set be given by the condition: if and only if . answer the following questions about 1) is reflexive? yes 2) is symmetric? yes 3) is transitive? yes 4) is an equivalence relation? yes

Answer 1

The relation described is reflexive, symmetric, transitive, and an equivalence relation.

Step-by-step explanation:

The relation described is reflexive, symmetric, transitive, and an equivalence relation.

A relation is reflexive if every element in the set is related to itself. In this case, the given condition holds true for every element, so the relation is reflexive.

A relation is symmetric if whenever a is related to b, then b is related to a. In this case, the given condition is bi-conditional, meaning if a is related to b, then b is related to a. Therefore, the relation is symmetric.

A relation is transitive if whenever a is related to b and b is related to c, then a is related to c. Since the given condition is bi-conditional, if a is related to b and b is related to c, then a is related to c. Therefore, the relation is transitive.

Since the relation is reflexive, symmetric, and transitive, it satisfies the properties of an equivalence relation.