Question

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?

Question 9 options:
a. It is both reflexive and symmetric
b. It is only reflexive
c. It is both reflexive and transitive
d. It is only antisymmetric

Answer 1

The relation under consideration exhibits both the reflexive and transitive properties, confirming option c as the correct choice.

Step-by-step explanation:

The relation being both reflexive and transitive means that it satisfies two properties:

1. Reflexive: For every element a in the set, (a, a) belongs to the relation.

2. Transitive: If (a, b) and (b, c) belong to the relation, then (a, c) also belongs to the relation.

Let's break down the properties:

- Reflexive: To check if the relation is reflexive, we examine if every element relates to itself. If (a, a) exists for all elements a in the set, the relation is reflexive.

- Transitive: To determine transitivity, we need to verify that for any elements a, b, and c, if (a, b) and (b, c) are in the relation, then (a, c) should also be in the relation.

Upon evaluating the given relation, it satisfies both conditions. For reflexivity, every element relates to itself (a, a). For transitivity, whenever (a, b) and (b, c) are in the relation, (a, c) holds true. Therefore, the relation is both reflexive and transitive, aligning with option c.