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## #17 - Rule Substitution

• PowerScore Staff
• Posts: 8314
• Joined: Feb 02, 2011
#82151
Complete Question Explanation

The correct answer choice is (E).

This explanation is still in progress. Please post any questions below!
kmclean
• Posts: 4
• Joined: Jan 05, 2021
#83263
Hi there PowerScore!

Can someone please explain why (D) is incorrect.

If Hu is nominee for councillor then that would make Jensen Mayor nominee and because Kuno cannot be nominated for councillor that would force them out.

I understand how (E) is correct but do not understand the error in (D).

Robert Carroll
• PowerScore Staff
• Posts: 1008
• Joined: Dec 06, 2013
#83274
kmac,

When evaluating answer choice (D), you said "because Kuno cannot be nominated for councillor that would force them out". But answer choice (D) says that if H is nominated for councillor, K isn't nominated at all; we don't have to use the fact that K can't be nominated for councillor to rid of K. Instead, K is out entirely when H is nominated for councillor.

You appear to be using the rule we're substituting for in the logic of answer choice (D). But we're not trying to prove that the rule we're substituting for makes answer choice (D) true - rather, the opposite. We want an answer that could be used instead of the original rule, and that, when combined with the other rules, would result in the game situation being the same.

What's good about answer choice (D) is that, if H is nominated for councillor, it puts K out entirely. But what if H is not nominated for councillor?

I wrote out a hypothetical situation:

J is nominated for mayor.
H is nominated for treasurer.
F and K are nominated for councillor.

That situation is consistent with every rule except the last rule. And remember, we're trying to substitute for that last rule. Answer choice (D) is not going to stop this hypothetical - H is not a nominee for councillor, so answer choice (D)'s sufficient condition is false, so nothing follows from it. There's now nothing that prevents my hypothetical from working. But my hypothetical shouldn't work - the last rule of the game disallows it. So if the last rule of the game were replaced by answer choice (D), a situation that shouldn't be allowed would now be allowed. That's why answer choice (D) is inadequate.

Robert Carroll
1997law
• Posts: 2
• Joined: Jul 21, 2021
#89020
Robert,

Basically, you are saying that when the contrapositive of answer choice D is taken, it does not give us the same results as the rule being substituted. It's that simple, isn't it?
Beatrice Brown
• PowerScore Staff
• Posts: 75
• Joined: Jun 30, 2021
#89079
Hi 1997! Great question

What Robert's hypothetical shows is that answer choice (D) only works as a substitute for the last rule when the sufficient condition occurs (H is a nominee for councillor), but not when the sufficient condition does not occur (H is not a nominee for councillor).

This is a bit different than saying that taking the contrapositive of answer choice (D) gives us a different result than the rule we're substituting for. Taking the contrapositive would mean "If K is not a nominee, then H is not a nominee for councillor." What Robert is referring to is taking a look at what happens if the sufficient condition does not happen.

Robert's hypothetical shows us that answer choice (D) does not always prevent K from being a nominee for councillor, which is the rule we want to substitute for. From answer choice (D), we know that if H is a nominee for councillor, then K cannot be a nominee (meaning K can't be a nominee for councillor or mayor). But if H is not a nominee for councillor, what do we know about K? We actually don't know anything about K then, and Robert's hypothetical shows a situation that is consistent with all of the rules and the rule proposed by answer choice (D) but violates the last rule that we're trying to substitute for. For a rule substitution question, we want to make sure that the new rule has the same effects as the old rule, but this hypothetical shows us that this isn't the case for answer choice (D).

I hope this helps, and let me know if you have any other questions!

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