Let A = {1, 2, 3}, B = { 2, 3, 4} , then which of the following is a function form A to B ? (a){(1,2),(1,3),(2,3),(3,3)} (b){(1,3),(2,4)} (c){(1,3),(2,2),(3,3)} (d){(1,2),(2,3),(3,2),(3,4)}

Options

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

Answer

To determine which of the given options represents a function from set A to set B, we need to ensure that each element in set A is mapped to exactly one element in set B.

Given:
- Set A = {1, 2, 3}
- Set B = {2, 3, 4}

### Step-by-Step Solution:

1. **Understanding the Definition of a Function**:
A function from set A to set B must assign each element in A to exactly one element in B. This means that for every x in A, there should be a unique y in B.

2. **Evaluating Each Option**:
We will evaluate each option to see if it satisfies the condition of being a function.

**Option (a)**: {(1, 2), (1, 3), (2, 3), (3, 3)}
- Here, the element 1 from A is mapped to both 2 and 3 in B. This violates the function rule (one input cannot have two outputs).
- **Conclusion**: Not a function.

**Option (b)**: {(1, 3), (2, 4)}
- The element 1 is mapped to 3, and 2 is mapped to 4. However, there is no mapping for the element 3 in A.
- **Conclusion**: Not a function (since not all elements of A are used).

**Option (c)**: {(1, 3), (2, 2), (3, 3)}
- Here, 1 is mapped to 3, 2 is mapped to 2, and 3 is mapped to 3. Each element in A has a unique mapping in B.
- **Conclusion**: This is a function.

**Option (d)**: {(1, 2), (2, 3), (3, 4)}
- The element 3 in A is mapped to 4 in B. However, there is no mapping for the element 1 in A.
- **Conclusion**: Not a function (since not all elements of A are used).

3. **Final Conclusion**:
The only option that satisfies the definition of a function from A to B is option (c): {(1, 3), (2, 2), (3, 3)}.

### Answer:
The correct answer is (c) {(1, 3), (2, 2), (3, 3)}.