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

Answer

To determine which of the given pairs are relations from set A to set B, we need to check if the first element of each pair is from set A and the second element is from set B.

Given:
- Set A = {a, b, c, d}
- Set B = {x, y, z}

The pairs we need to evaluate are:
1. (a, x)
2. (y, d)
3. (x, c)

### Step-by-Step Solution:

**Step 1:** Check the first pair (a, x).
- The first element is 'a', which is in set A.
- The second element is 'x', which is in set B.
- Since both elements satisfy the condition (first from A and second from B), (a, x) is a valid relation from A to B.

**Step 2:** Check the second pair (y, d).
- The first element is 'y', which is in set B.
- The second element is 'd', which is in set A.
- This does not satisfy the condition (first should be from A and second from B), so (y, d) is not a valid relation from A to B.

**Step 3:** Check the third pair (x, c).
- The first element is 'x', which is in set B.
- The second element is 'c', which is in set A.
- This also does not satisfy the condition (first should be from A and second from B), so (x, c) is not a valid relation from A to B.

### Conclusion:
The only valid relation from set A to set B is (a, x).

### Final Answer:
The relation from A to B is: {(a, x)}

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