Given `A={2,3,4},B={2,5,6,7}`, construct an example of each the following. A mapping from A to B which is not one-one

Answer

To construct a mapping from set A to set B that is not one-one, we need to ensure that at least two elements from set A map to the same element in set B.

### Step-by-Step Solution:

1. **Identify the Sets**:
- Let \( A = \{2, 3, 4\} \)
- Let \( B = \{2, 5, 6, 7\} \)

2. **Understanding One-One Function**:
- A function is one-one (injective) if every element of set A maps to a unique element in set B. This means no two different elements in A can map to the same element in B.

3. **Creating a Many-One Mapping**:
- To create a mapping that is not one-one, we need at least two elements from A to map to the same element in B.

4. **Example of a Mapping**:
- Let's define a mapping \( f: A \to B \) as follows:
- \( f(2) = 5 \)
- \( f(3) = 5 \)
- \( f(4) = 6 \)

5. **Check the Mapping**:
- In this mapping:
- Both \( 2 \) and \( 3 \) from set A map to \( 5 \) in set B.
- \( 4 \) maps to \( 6 \).
- Since two different elements from A (2 and 3) map to the same element in B (5), this mapping is not one-one.

### Final Mapping:
- The mapping can be summarized as:
- \( f = \{(2, 5), (3, 5), (4, 6)\} \)