Relations

Step 1: To determine the type of relation, we need to analyze the properties of the given relation $R$ on the set $%5C%7Ba%2C%20b%2C%20c%5C%7D$ . The relation $R$ is defined as: $R%20%3D%20%5C%7B(a%2C%20a)%2C%20(b%2C%20b)%2C%20(c%2C%20c)%2C%20(a%2C%20c)%5C%7D.$

Step 2: Check for the following properties:
- Reflexive: A relation is reflexive if for every element $x%20%5Cin%20S$ , $(x%2C%20x)$ belongs to the relation. In this case, $(a%2C%20a)%2C%20(b%2C%20b)%2C%20(c%2C%20c)$ are in the relation, so the relation is reflexive.
- Symmetric: A relation is symmetric if for every pair $(x%2C%20y)$ in the relation, the pair $(y%2C%20x)$ is also in the relation. Since $(a%2C%20c)$ is in the relation but $(c%2C%20a)$ is not, the relation is not symmetric.
- Transitive: A relation is transitive if whenever $(x%2C%20y)$ and $(y%2C%20z)$ are in the relation, $(x%2C%20z)$ must also be in the relation. Since $(a%2C%20c)$ is in the relation but there is no corresponding $(c%2C%20a)$ , the relation is not transitive.

Step 3: The relation is reflexive but not symmetric or transitive, which makes it spontaneous, traditional, but not conformist. Thus, the relation $R$ is spontaneous, traditional, but not conformist.

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Relations

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs