The set of numbers which are multiples of 5 is :

Options

A. a finite set
B. an infinite set
C. a universal set
D. None of these.

Answer

To find the set of numbers that are multiples of 5, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Multiples of 5**:
- A multiple of a number is obtained by multiplying that number by an integer. For example, the multiples of 5 can be found by multiplying 5 with integers (0, 1, 2, 3, ...).

2. **Listing the First Few Multiples of 5**:
- Start with the integer 0 and multiply it by 5:
- \( 5 \times 0 = 0 \)
- Next, multiply 5 by 1:
- \( 5 \times 1 = 5 \)
- Then multiply 5 by 2:
- \( 5 \times 2 = 10 \)
- Continue this process:
- \( 5 \times 3 = 15 \)
- \( 5 \times 4 = 20 \)
- \( 5 \times 5 = 25 \)
- \( 5 \times 6 = 30 \)
- \( 5 \times 7 = 35 \)
- \( 5 \times 8 = 40 \)

3. **Recognizing the Pattern**:
- From the calculations, we see that the multiples of 5 are:
- \( 0, 5, 10, 15, 20, 25, 30, 35, 40, \ldots \)

4. **Identifying the Infinite Nature of the Set**:
- Since you can keep multiplying 5 by larger integers indefinitely, the set of multiples of 5 does not have an upper limit. Therefore, it is an infinite set.

5. **Expressing the Set in Set Notation**:
- The set of multiples of 5 can be expressed as:
\[ \{ 5n \mid n \in \mathbb{Z} \} \]
- Here, \( n \) represents any integer (positive, negative, or zero).

### Final Answer:
The set of numbers which are multiples of 5 is:
\[ \{ 0, 5, 10, 15, 20, 25, 30, 35, 40, \ldots \} \text{ or } \{ 5n \mid n \in \mathbb{Z} \} \]