If A = {(a, b, c, l, m, n}, then the maximum number of elements in any relation on A, is

Options

A. 12
B. 16
C. 32
D. 36

Answer

To find the maximum number of elements in any relation on the set A, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Set A**:
We have the set A = {a, b, c, l, m, n}.

2. **Count the Number of Elements in A**:
The number of elements in set A, denoted as n, is 6 because there are six distinct elements: a, b, c, l, m, and n.

3. **Understand the Concept of Relations**:
A relation on a set A is a subset of the Cartesian product A × A. The Cartesian product A × A consists of all possible ordered pairs (x, y) where x and y are elements of A.

4. **Calculate the Size of the Cartesian Product A × A**:
The size of the Cartesian product A × A is given by n × n, which is 6 × 6 = 36. This means there are 36 possible ordered pairs.

5. **Determine the Maximum Number of Elements in a Relation**:
The maximum number of elements in any relation on set A is equal to the total number of ordered pairs in A × A. Therefore, the maximum number of elements in any relation on A is 36.

### Final Answer:
The maximum number of elements in any relation on A is **36**.

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