soyeonjeon Wrote:I do not get 13, 14 and 16.
I do not understand the first rule, what would be the contrapositive of the first rule? I would assume that its contrapositive would be if the moderates voted differently from the two conservatives and at least one liberal. I would assume that the contrapositive of this rule would NOT be that if the two moderates did not vote the same way..then..bla.
But I might be wrong, which is why I am not able to solve 13 or 14 or 16.
You are closer than you think understanding the first rule.
CC and at least one L vote same way ---> MM votes same way with them
The contrapositive of the rule can be triggered by either scenario you mentioned. If it is not true that MM voted together, then you would trigger the contrapositive. There is no way that CC and at least 1 L votes the same way because this would force the two M's to be together.
So the contrapositive could be triggered simply by knowing that AT LEAST 1 M fails to vote with the CCL group. Both M's failing to do that will of course trigger it.
With both conditional rules in this game, simply knowing that the C's voted differently or the M's voted differently amongst its own group would be sufficient to know the contrapositive is triggered.
In other words, consider the LLL ---> CC votes opposite way rule.
If the C's vote differently from each other, then you are denying a requirement of all L's voting together.
For 14, I do not see how to solve it other than to try to disprove every answer choice as indicated in one of the comments.
For 16, I do not see how we get narrowed down to two possibilities as mentioned in one of the comments.
If you did not make the upfront inference about L in this game, then I would save a question like 14 for last so that previous work can do the work for us.
The fact that we are given that at least one C voted against should trigger your interest. What do we know if LLL votes the same way? No C votes that way. So could we have all L's votes against? Nope, we have a C there. So we know that at least one L must always vote for.
So for 16, we are given a fixed distribution for the 7 judges. 5 for, 2 against.
_ _ _ _ _ .... C _
We know that since we have LLL and MM...we know that at least 2 LL and 1 M will be in. There is only one slot left in the out column.
L L M _ _ .... C _
So we now have L M C left to place. We only have one rule left, which is the LLL ---> No C that way rule. The other rule, that is now void, was the CC and at least 1 L vote the same way rule. We know that this rule can never be triggered in this scenario.
So we can use the LLL rule in placing our last 3 variables. You could also use any of C, M, L in a "scenario of 2" situation. In other words, you have this below:
L L M _ _ .... C _
We know that we have CML left to place. We can pick any of those variables and have a situation of it voting for....then a situation of it voting against. This would show all of our possibilities. We must consider the LLL rule while doing that however. I will pick L to use in my scenario of 2.
L voting for:
L L M L M .... C C
L voting against:
L L M M C .... C L
As we can see, in either scenario, it must be true that both M's vote for.