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

Answer

To determine whether the given relation \(\{(z,x),(z,y),(x,a)\}\) is a relation from set \(B\) to set \(A\), we need to analyze the elements of the relation in the context of the sets \(A\) and \(B\).

### Step-by-Step Solution:

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

2. **Understand the Definition of a Relation**:
- A relation from set \(B\) to set \(A\) consists of ordered pairs where the first element is from set \(B\) and the second element is from set \(A\).

3. **Examine Each Ordered Pair**:
- The given relation is \(\{(z,x),(z,y),(x,a)\}\).
- We will check each ordered pair to see if it meets the criteria of having the first element from \(B\) and the second element from \(A\).

4. **Check the First Ordered Pair \((z,x)\)**:
- First element: \(z\) (from \(B\)) - **Valid**
- Second element: \(x\) (not in \(A\)) - **Invalid**

5. **Check the Second Ordered Pair \((z,y)\)**:
- First element: \(z\) (from \(B\)) - **Valid**
- Second element: \(y\) (not in \(A\)) - **Invalid**

6. **Check the Third Ordered Pair \((x,a)\)**:
- First element: \(x\) (not in \(B\)) - **Invalid**
- Second element: \(a\) (from \(A\)) - **Valid**

7. **Conclusion**:
- Since none of the ordered pairs in the relation \(\{(z,x),(z,y),(x,a)\}\) have both elements satisfying the requirement of being from \(B\) and \(A\) respectively, we conclude that this relation is **not a relation from \(B\) to \(A\)**.

### Final Answer:
The relation \(\{(z,x),(z,y),(x,a)\}\) is **not a relation from \(B\) to \(A\)**.

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