Let `R` be a relation from a set A to a set B, then

Options

A. A. `R=AuuB`
B. B. `R=AnnB`
C. C. `RsubeAxxB`
D. D. `RsubeBxxA`

Answer

To solve the question, we need to analyze the relation \( R \) defined from set \( A \) to set \( B \) and determine which of the given options is correct.

### Step-by-Step Solution:

1. **Understanding the Relation**:
- A relation \( R \) from set \( A \) to set \( B \) consists of ordered pairs \( (x, y) \) where \( x \in A \) and \( y \in B \).
- This means that \( R \) is a subset of the Cartesian product \( A \times B \).

2. **Identifying the Cartesian Product**:
- The Cartesian product \( A \times B \) is defined as the set of all possible ordered pairs \( (x, y) \) such that \( x \) belongs to \( A \) and \( y \) belongs to \( B \).
- Therefore, \( A \times B = \{ (x, y) | x \in A, y \in B \} \).

3. **Analyzing the Options**:
- **Option A**: \( R = A \cup B \) - This is incorrect because \( R \) consists of ordered pairs, not individual elements from \( A \) or \( B \).
- **Option B**: \( R = A \cap B \) - This is also incorrect for the same reason; \( R \) cannot be the intersection of two sets.
- **Option C**: \( R \subseteq A \times B \) - This is correct because \( R \) is defined as a relation from \( A \) to \( B \), meaning it must consist of pairs from \( A \times B \).
- **Option D**: \( R \subseteq B \times A \) - This is incorrect because \( R \) is defined from \( A \) to \( B \), not the other way around.

4. **Conclusion**:
- The correct option is **C**: \( R \subseteq A \times B \).

### Final Answer:
The correct option is **C**: \( R \) is a subset of \( A \times B \).