Let A = {2, 3, 5}, B = (10, 12, 15}, then which of the following is a function from A to B ?

Options

A. {(2, 10), (2, 12), (2, 15)}
B. {(2, 10), (3, 12), (3, 15)}
C. {(2, 12), (3, 10), 5, 10)}
D. {(2, 10), (3, 12), (3,15), (5, 15)}

Answer

To determine which of the given options represents a function from set A to set B, we need to ensure that the mapping satisfies the properties of a function. A function must be both one-to-one (injective) and onto (surjective).

Given:
- Set A = {2, 3, 5}
- Set B = {10, 12, 15}

### Step-by-step Solution:

1. **Understanding the Definition of a Function**:
A relation from set A to set B is a function if:
- Each element in A maps to exactly one element in B (one-to-one).
- Each element in B is mapped by at least one element in A (onto).

2. **Analyzing Each Option**:
We will check each option to see if it satisfies the criteria for being a function.

**Option 1**:
- 2 → 10
- 2 → 12
- 2 → 15
- **Analysis**: The element 2 from set A maps to multiple elements in set B (10, 12, and 15). This violates the one-to-one condition.
- **Conclusion**: Not a function.

**Option 2**:
- 2 → 10
- 3 → 12
- 3 → 15
- **Analysis**: The element 3 from set A maps to multiple elements in set B (12 and 15). This also violates the one-to-one condition.
- **Conclusion**: Not a function.

**Option 3**:
- 2 → 12
- 3 → 10
- 5 → 15
- **Analysis**: Each element in set A maps to a unique element in set B.
- 2 maps to 12
- 3 maps to 10
- 5 maps to 15
- All elements in A have distinct images in B, satisfying the one-to-one condition.
- **Conclusion**: This is a function.

**Option 4**:
- 2 → 10
- 3 → 12
- 3 → 15
- **Analysis**: The element 3 from set A maps to multiple elements in set B (12 and 15). This violates the one-to-one condition.
- **Conclusion**: Not a function.

3. **Final Conclusion**:
After analyzing all options, we find that **Option 3** is the only valid function from set A to set B.

### Answer:
**Option 3 is a function from A to B.**