# 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

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?

Replies

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 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