If A = {a,b,c,d}, B = {1,2,3}, Which of the following sets of ordered pairs are not relations from A to B ?

Options

A. {(a,1), (a, 3) }
B. { (b,1), (c, 2), (d, 1)}
C. { (a,2),(b,3),(3,b)}
D. {(a,1),(b,2),(c,3)}

Answer

To determine which of the given sets of ordered pairs are not relations from set A to set B, we first need to understand what a relation from A to B is. A relation from set A to set B consists of ordered pairs where the first element comes from set A and the second element comes from set B.

Given:
- Set A = {a, b, c, d}
- Set B = {1, 2, 3}

Now, let's analyze the options provided (though not explicitly listed in the question, we will assume some common options):

### Step 1: Identify the options
Assuming the options are:
1. Option A: {(a, 1), (a, 3)}
2. Option B: {(b, 1), (c, 2), (d, 1)}
3. Option C: {(a, 2), (b, 2), (3, b)}

### Step 2: Check each option for valid relations
- **Option A: {(a, 1), (a, 3)}**
- Here, both ordered pairs have the first element from A (a) and the second elements from B (1, 3).
- This is a valid relation from A to B.

- **Option B: {(b, 1), (c, 2), (d, 1)}**
- In this case, all ordered pairs have the first elements from A (b, c, d) and the second elements from B (1, 2).
- This is also a valid relation from A to B.

- **Option C: {(a, 2), (b, 2), (3, b)}**
- The first two ordered pairs have their first elements from A (a, b) and second elements from B (2).
- However, the third ordered pair (3, b) has the first element 3, which is from set B, not A.
- Therefore, this does not satisfy the condition of being a relation from A to B.

### Conclusion
The set of ordered pairs that is **not a relation from A to B** is **Option C**: {(a, 2), (b, 2), (3, b)}.