Question

If $R$ is a relation from a set $A$ to set $B$ and $S$ is a relation from $B$ to a set $C$, then the relation $S\circ R$

• A. Is from $A$ to $C$
• B. Is from $C$ to $A$
• C. Does not exist
• D. None of these

Answer 1

The correct option is A

Is from $A$ to $C$

Finding the relation $S\circ R$:

If $R$ is a relation from a set $A$ to set $B$ then it is a subset of $A\times B$, where the subset is represented by $\subseteq$

Here $R\subseteq A\times B$ and $S\subseteq B\times C$

Therefore,

$S\circ R=\{(a,c)\in A\times C|b\in B:(a,b)\in R,(b,c)\in S\}$

$S\circ R$ is from set $A$ to set $C$.

Hence, the correct option is (A).