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Let $M$ be the number of relations on $\{1,2,3\}$ that make it into a directed set, and let $N$ be the number of equivalence relations on $\{1,2,3\}$.

What is $M+N$?

A

$19$

B

$20$

C

$21$

D

$22$

E

$23$

F

24

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