If set A has 3 elements and the set B has 5 elements , then , the number of injective mappings that can be defined from A to B is :

Options

A. 60
B. 120
C. 240
D. 360

Answer

To find the number of injective mappings (one-to-one functions) from set A to set B, we can follow these steps:

1. **Identify the sizes of the sets**:
- Set A has 3 elements.
- Set B has 5 elements.

2. **Understand the concept of injective mappings**:
An injective mapping means that each element in set A must map to a unique element in set B. No two elements in set A can map to the same element in set B.

3. **Choose an element from set B for each element in set A**:
- For the first element in set A (let's call it A1), we have 5 choices from set B (U, V, W, X, Y).
- For the second element in set A (A2), since we cannot use the element already chosen for A1, we have 4 remaining choices.
- For the third element in set A (A3), we cannot use the elements chosen for A1 and A2, leaving us with 3 choices.

4. **Calculate the total number of injective mappings**:
The total number of injective mappings can be calculated by multiplying the number of choices for each element:
\[ \text{Total injective mappings} = 5 \times 4 \times 3 \]

5. **Perform the multiplication**:
\[ 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]

6. **Conclusion**:
Therefore, the total number of injective mappings from set A to set B is 60.

### Summary of Steps:
1. Identify the sizes of sets A and B.
2. Understand injective mappings.
3. Choose elements from set B for each element in set A.
4. Calculate the total number of mappings by multiplying the choices.
5. Perform the multiplication to get the final answer.