Consider two relations on the set $\{1, 2, 3, 4\}$. The relations R and S are given by $R = \{(1, 2),(1, 3),(2,3),(2, 4),(3, 1)\}$ and $S = \{(2, 1),(3, 1),(3, 2),(4, 2)\}$.

(a) Determine $S ◦ R$ (b) Determine $R ◦ S$ (c) Draw directed graphs representations of $S, R, S ◦ R,$ and $R ◦ S$. (d) Determine the elements of $R ◦ R, R ◦ R ◦ R$, and $R ◦ R ◦ R ◦ R$.

<aside> 💡 (a)

$$ S \circ R = \{(2,2),(2,3),(3,2),(3,3),(3,4),(4,3)\} $$

(b)

$$ R \circ S = \{ (1,1),(1,2),(2,1),(2,2) \} $$

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(c)

$$ R:\\\dArr $$

$$ S:\\\dArr $$

$$ S \circ R:\\\dArr $$

$$ R\circ S:\\\dArr $$

(d)

$$ R ◦ R=\{(1,1),(1,3),(1,4),(2,1)\\ R\circ R\circ R=\{(1,1),(1,2),(1,3),(1,4)\}\\ R\circ R\circ R\circ R=\{(1,1),(1,2),(1,3),(1,4)\} $$