Which of the following are relations from B to A, where `A={a,b,c,d}` and `B={x,y,z}?`
`{(x,d),(y,c),(z,b)}`

Answer

To determine whether the given relation \(\{(x,d),(y,c),(z,b)\}\) is a relation from set \(B\) to set \(A\), we need to check if the first elements of the ordered pairs belong to set \(B\) and the second elements belong to set \(A\).

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set \(A = \{a, b, c, d\}\)
- Set \(B = \{x, y, z\}\)

2. **List the Given Relation**:
- The given relation is \(\{(x,d), (y,c), (z,b)\}\).

3. **Check Each Ordered Pair**:
- For the pair \((x,d)\):
- First element \(x\) is from set \(B\) (which is correct).
- Second element \(d\) is from set \(A\) (which is also correct).
- For the pair \((y,c)\):
- First element \(y\) is from set \(B\) (correct).
- Second element \(c\) is from set \(A\) (correct).
- For the pair \((z,b)\):
- First element \(z\) is from set \(B\) (correct).
- Second element \(b\) is from set \(A\) (correct).

4. **Conclusion**:
- Since all the first elements of the ordered pairs are from set \(B\) and all the second elements are from set \(A\), the relation \(\{(x,d), (y,c), (z,b)\}\) is indeed a relation from \(B\) to \(A\).

### Final Answer:
The relation \(\{(x,d), (y,c), (z,b)\}\) is a relation from \(B\) to \(A\).

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