If `A={a,b,c,d},B={1,2,3}`, find whether or not the following sets of orderd pairs are relations from A to B or not
`R_(3)={(a,1),(b,2),(3,c)}`

Answer

To determine whether the set of ordered pairs \( R_3 = \{(a, 1), (b, 2), (3, c)\} \) is a relation from set \( A \) to set \( B \), we need to check if all the first elements of the ordered pairs (the x-coordinates) belong to set \( A \) and all the second elements (the y-coordinates) belong to set \( B \).

### Step-by-Step Solution:

1. **Identify the sets**:
- Set \( A = \{a, b, c, d\} \)
- Set \( B = \{1, 2, 3\} \)

2. **Examine the ordered pairs in \( R_3 \)**:
- The ordered pairs are \( (a, 1) \), \( (b, 2) \), and \( (3, c) \).

3. **Check the first elements (x-coordinates)**:
- For \( (a, 1) \):
- \( a \) is in set \( A \).
- For \( (b, 2) \):
- \( b \) is in set \( A \).
- For \( (3, c) \):
- \( 3 \) is **not** in set \( A \).

4. **Conclusion about the first elements**:
- Since \( 3 \) is not an element of set \( A \), the first element of the ordered pair \( (3, c) \) does not belong to set \( A \).

5. **Final determination**:
- Since not all first elements of the ordered pairs belong to set \( A \), the set \( R_3 \) is **not** a relation from \( A \) to \( B \).

### Final Answer:
The set of ordered pairs \( R_3 \) is not a relation from set \( A \) to set \( B \).