If Tampa hosts two of the meetings, which one of the following could be true?
Saksham-Sabarwalon December 28, 2021
Question 16
Can you please explain this question because I'm not able to understand that how V cannot go in Fall because there is a conditions which says that, If T is in Fall then V will be in Fall.
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I will first explain how to do this question, and then show what I believe caused the confusion.
Original Setup:
HMOTV
Fall: _ _ _ Spr: _ _ _
The game has five letters, H M O T V, all of which must be placed at least once. Since we have exactly six spaces, we know that exactly one letter will be placed twice, and the rest will go once. This question tells us that T hosts two meetings, and since they cannot host two meetings in the same semester, T must be in both seasons.
Fall: T _ _ Spr: T _ _
Next, we know that either M or V must host each semester. Since we already have our repeat variable, T, we know that M and V cannot repeat, so one of them will be in fall and the other will be in spring.
Fall: T M/V _ Spr: T M/V _
This leaves only O and H for the remaining spaces:
Fall: T M/V O/H Spr: T M/V O/H
Now, we can make scenarios with the remaining rules. One rule says Hf ? Mf. So we can make one in which the H is in fall, and the other in which H is in spring:
Scenario 1 (H in fall):
Fall: T M/V H Spr: T M/V O
Then, because of the Hf ? Mf rule, we know M is in fall, leaving V for spring:
Fall: T M H Spr: T V O
Scenairo 2 (H not in fall)
Fall: T M/V O Spr: T M/V H
These represent every possible setup. Only answer choice B is possible given these boards.
I believe what you did is diagram:
Vs ? Ts
and then take the contrapositive as:
Tf ? Vf
If each piece could only be placed once, this would be correct, because if T wasn’t in spring that would prove that it is in fall. However, since T can be placed multiple times, T not being in spring is not the same as T being in fall. Your contrapositive should instead look like this:
T not in spring ? V not in spring
On this particular question, T IS in spring, so the contrapositive would not trigger. With the incorrect contrapositive above, we would mistakingly assume that V is must be in fall.
