Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following is a function from A to B ?

Options

A. {(1, 2), (1, 3), (2, 3), (3, 3)}
B. {(1, 3), (2, 4)}
C. {(1, 3), (2, 3), (3,3)}
D. {(1, 2), (2, 3), (3,4), (3, 2)}

Answer

To determine which of the given options is a function from set A to set B, we first need to understand the definition of a function. A function from set A to set B assigns each element in A exactly one element in B.

### Step-by-Step Solution:

1. **Identify the Sets**:
- Let \( A = \{1, 2, 3\} \)
- Let \( B = \{2, 3, 4\} \)

2. **Understanding Function Requirements**:
- A function \( f: A \to B \) must assign each element in A to exactly one element in B. This means no element in A can be associated with more than one element in B.

3. **Examine Possible Functions**:
- We need to check the options provided (though they are not specified in the question). We will consider a generic approach to evaluate if a mapping is a function.

4. **Mapping Elements**:
- For each element in A (1, 2, 3), we can map it to elements in B (2, 3, 4).
- Example mappings could be:
- \( f(1) = 2, f(2) = 3, f(3) = 4 \)
- \( f(1) = 3, f(2) = 3, f(3) = 2 \)
- \( f(1) = 4, f(2) = 4, f(3) = 4 \)

5. **Check for Valid Functions**:
- We need to ensure that each element in A has a unique image in B:
- If \( f(1) = 3, f(2) = 3, f(3) = 3 \) is a valid function because all elements in A map to the same element in B (3).
- If any mapping assigns an element in A to more than one element in B, it is not a function.

6. **Select the Correct Option**:
- Based on the analysis, if one of the options is \( f(1) = 3, f(2) = 3, f(3) = 3 \), then this is a valid function from A to B.

### Conclusion:
The correct option that represents a function from A to B is the one where each element of A maps to exactly one element in B, even if multiple elements in A map to the same element in B.