If 2+2=5, the moon is made of green cheese

Known facts :

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1. Santa Claus does $NOT$ exist.
2. $3691$ $IS$ a prime.

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Now let's take a closer look at the choices ...

$\quad$ Choice A: If $3691$ is composite, the Santa Claus exists. $\quad$

Reasoning: $3691$ is NOT composite and therefore the statement is not false.

$\quad$ Choice B: If $3691$ is composite,the Santa Claus does not exist. $\quad$

Reasoning: $3691$ is NOT composite but that doesn't force Santa not to exist does?!The statement only implies that "IF (so) ,THEN (that)" but does not necessarily imply "IF (not) , THEN (that) is false ".

$\quad$ Choice C: If $3691$ is prime, the Santa Claus exists. $\quad$

Reasoning: $3691$ is a prime indeed and hence Santa Claus must exist which contradicts our no. 1 fact.

$\quad$ Choice D: If $3691$ is prime,the Santa Claus does not exist. $\quad$

Reasoning: $3691$ is a prime and Santa Claus does not exist,no argument here!