If R is a relation from a set A to a set B and S is a relation from B to a set C, then the relation `SoR` a) is from A to C b) is from C to A c) does not exist d) None of these

Options

A. is from A to C
B. is from C to A
C. does not exist
D. None of these

Explanation

To solve the problem, we need to analyze the relations given in the question and determine the nature of the composition of these relations.

### Step-by-Step Solution:

1. **Understanding the Relations**:
- We are given two relations:
- \( R \) is a relation from set \( A \) to set \( B \).
- \( S \) is a relation from set \( B \) to set \( C \).

2. **Defining the Relations**:
- The relation \( R \) can be represented as a subset of the Cartesian product \( A \times B \). This means \( R \subseteq A \times B \).
- The relation \( S \) can be represented as a subset of the Cartesian product \( B \times C \). This means \( S \subseteq B \times C \).

3. **Composition of Relations**:
- The composition of the relations \( S \) and \( R \), denoted as \( S \circ R \), is defined as follows:
- For any element \( a \in A \) and \( c \in C \), the pair \( (a, c) \) is in the relation \( S \circ R \) if there exists some \( b \in B \) such that \( (a, b) \in R \) and \( (b, c) \in S \).

4. **Resulting Relation**:
- From the definition of the composition, we can conclude that \( S \circ R \) is a relation from set \( A \) to set \( C \) because it connects elements from \( A \) to elements in \( C \) through the intermediary set \( B \).

5. **Conclusion**:
- Therefore, the relation \( S \circ R \) is indeed a relation from \( A \) to \( C \).

### Final Answer:
- The correct option is **a) is from A to C**.