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

Answer

To determine if the given set of ordered pairs \((x,b)\) and \((y,a)\) is a relation from set \(B\) to set \(A\), we need to follow these steps:

### Step 1: Identify the Sets
We have two sets:
- Set \(A = \{a, b, c, d\}\)
- Set \(B = \{x, y, z\}\)

### Step 2: Understand the Definition of a Relation
A relation from set \(B\) to set \(A\) is a subset of the Cartesian product \(B \times A\). This means that each ordered pair in the relation should have its first element from set \(B\) and its second element from set \(A\).

### Step 3: Analyze the Given Relation
The given relation is:
\[ \{(x,b), (y,a)\} \]
We need to check if both ordered pairs fit the definition of a relation from \(B\) to \(A\).

### Step 4: Check Each Ordered Pair
1. For the ordered pair \((x,b)\):
- The first element \(x\) is from set \(B\) (which contains \(x, y, z\)).
- The second element \(b\) is from set \(A\) (which contains \(a, b, c, d\)).
- Therefore, \((x,b)\) is a valid pair in the relation from \(B\) to \(A\).

2. For the ordered pair \((y,a)\):
- The first element \(y\) is from set \(B\).
- The second element \(a\) is from set \(A\).
- Therefore, \((y,a)\) is also a valid pair in the relation from \(B\) to \(A\).

### Step 5: Conclusion
Since both ordered pairs \((x,b)\) and \((y,a)\) have their first elements from set \(B\) and their second elements from set \(A\), we conclude that the given set of pairs is indeed a relation from \(B\) to \(A\).

### Final Answer
Yes, the set \(\{(x,b), (y,a)\}\) is a relation from \(B\) to \(A\).

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