Which one of the following, if substituted for the constraint that if Jaramillo is assigned to one of the ambassadors...

Mazen on April 27, 2022

Reason for eliminating C please?

Answer-choice C states: "If Ong is not assigned to an ambassadorship, then Kayne is assigned to an ambassadorship." Under the initial rules of the game setup: either O or K must be "in," or they cannot both be "out," which ironically is the wrong answer-choice C. If both O and K are out, then the contrapositive to rule 2 would also force J "out." But since we do not have an extra "out" space for J, answer-choice C is very tempting!!!!!! The only thing I can think of for eliminating C is the following (but I am not confident): Not taking into account the other rules, answer-choice C leaves the possibility for both O and K to be out, which is impossible because of the contrapositive to rule 2: if K is out, then J is out, but there are no more "out" spots because of the distribution dictates three "in" corresponding to V, Y, and Z, and two "out", But with answer-choice C we have a possibility (a could be true) of all three O, K, and J being out; not enough space on the outside or leaving one embassy unassigned which contrary to the setup. Is this why C should be eliminated?

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Mazen on April 27, 2022

Please ignore the above post. I figured it out:

Rule 2: J---->K
The contrapositive to Rule 2: ~k---->~J

When we combine Answer-choice D (J---->~N) or its contrapositive (N---->~J) combines with Rule 1 we end up with with the rule for which we substituted, i.e. Rule 2:
J---->~N combines with Rule 1 ~N---->K to effect J---->K, the contrapositive of which is ~K---->~J which is the contrapositive to Rule 2.

Answer-choice C is irrelevant in so far as tying J and K in accordance to Rule 2 while simultaneously substituting for it.

It helps to think through these more complex questions by reasoning our thoughts via posting!

Thank you

Thank you

Emil-Kunkin on May 4, 2022

Good Job Mazen,

I agree that the act of writing out your reasoning can help you to see what you may have missed or misinterpreted the first time