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Given two relations, $R \subseteq X \times Y$, and $S \subseteq Y \times Z$, where

$R := \{ (a,1), (b,1), (b,3), (c, 1), (c, 3), (d, 3) \}$
$S := \{ (1,D), (1, E), (2, B), (2,C), (3, A) \}$

Given the above two relations, which of the following options describes the composite relation $S \circ R \subseteq X \times Z$?

A

$\{(D,1), (E,1), (D,a), (E,a) \}$

B

$\{(a,D), (a,E), (b, A), (b,D), (b,E), (c,A), (c, D), (c,E), (d,A) \}$

C

$\{ (a,E), (b,D), (c,D), (d,A) \}$

D

$\{ (D,a), (E,a), (A,b), (D,b), (E,b), (D,c), (E,c) \}$

E

$\{ (d,A), (a,D), (c,D), (b,C) \}$

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