Let `A={a,b,c}` and `B={1,2}`. Consider a relation `R` defined from st A to set B. Then `R` can equal to set

Options

A. A
B. B
C. `AxxB`
D. `BxxA`

Explanation

To solve the problem, we need to understand the concept of a relation defined from one set to another.

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

A relation R from set A to set B is defined as a subset of the Cartesian product A × B. The Cartesian product A × B consists of all possible ordered pairs (x, y) where x is an element from set A and y is an element from set B.

### Step-by-step Solution:

1. **Determine the Cartesian Product A × B**:
- The Cartesian product A × B is formed by pairing each element of A with each element of B.
- Thus, A × B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}.

2. **Understanding the Relation R**:
- A relation R from A to B can be any subset of the Cartesian product A × B. This means R can contain none, some, or all of the pairs from A × B.

3. **Identifying Possible Relations**:
- Since R can be any subset of A × B, it can be:
- The empty set: R = {}
- A single pair: R = {(a, 1)}, R = {(b, 2)}, etc.
- Multiple pairs: R = {(a, 1), (b, 1)}, R = {(a, 2), (c, 2)}, etc.
- All pairs: R = A × B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}.

4. **Conclusion**:
- Therefore, the relation R can equal any subset of A × B, which means it can take on many forms.

### Final Answer:
The relation R can equal any subset of the set A × B, which is {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}.