MAYOR AND SEVEN AMENDMENTS

[nicolle828]

I am re-watching the Advanced Logic Games series by Dave Killoran and have what feels like a silly question. I understand exactly what he did in this set-up, but am wondering in the conditional rule where if 6 and 1 are rejected and therefore 2 or 5 are accepted. Can they both be accepted when it says "or"? Because if they can't, then 1, 6, 7, and 3/4 would be rejected so all four spots will be filled and there will be no room for 2 or 5 so we would know even more. If "or" means only one can be accepted, then it has to be the opposite conditional used and we know much more about the set-up with the only actual remaining unknown being whether 3 and 4 is accepted or rejected.

[Nikki Siclunov]

Hi Nicolle,

In ordinary language, "or" can mean the inclusive or exclusive "or." In some instances, "or" would clearly be exclusive (e.g. "Tom is either guilty or not" - clearly, he can't be both); in other instances, "or" would be inclusive (e.g. "Your success is due to either competence or good luck" - possibly both).

In logic, however, the logical connective "or" is, by default, inclusive, that is, it allows for the possibility of both operands to be true unless explicitly instructed otherwise (usually with a "not both" clause). So, the conditional statement you mention allows for the possibility of both 2 and 5 to be accepted. If the rule wanted to exclude such a possibility, it would have said, "If 6 and 1 are rejected, then either 2 or 5, but not both, is accepted."

The contrapositive of the rule you mention would be this:

If 2 and 5 are rejected (i.e. neither 2 nor 5 are accepted), then either 6 or 1 (or both) are accepted.

Does that make sense? Let me know.

Thanks!

[nicolle828]

Nikki,

The "or" statement I'm referring to is not stated or part of a provided statement, but an inference as a result of the contrapositive so there was no place for it to say "but not both" so that was the reason why I was wondering if it is not specifically stated when there is an "or" then the two can actually both be chosen together? I know that sounds confusing upon reading but that is exactly what happened in this set up.

Thanks again!

Nicolle

[Morgan O'Donnell]

Hi Nicolle!

In order to assist you a little better, can you tell us what game you are referring to in your initial post? The preptest it comes from and the question number would be super helpful!

Once we have that, it will be much clearer

Thanks so much!!

Morgan O'Donnell
PowerScore Test Prep

[nicolle828]

Hi Morgan!

It's in Dave's Advanced Logic course, but he doesn't say anything about what LSAT it is from so I am uncertain how to answer your question. Sorry!!

Nicolle

[Nikki Siclunov]

Hi Nicolle,

If the statement in question is an inference as a result of a contrapositive, can you provide us with the original rule itself? Once we have that, we can tell you whether the contrapositive you're asking about entails an inclusive or an exclusive use of the connective.

Thanks,

Nikki

[nicolle828]

This is the game as it is written in the Advanced Logic Course.

A mayor is considering seven amendments- 1, 2, 3, 4, 5, 6, and 7- to her town's zoning laws The mayor will either approve or reject each of the seven amendments. The following is known about the approvals and rejections:
The mayor approves exactly one of amendments 3 and 4.
If amendments 2 and 5 are rejected, amendment 6 is approved.
At least three of the amendments are approved, and at least three of the amendments are rejected.
Amendment 1 and 6 are either both approved or both rejected.
Amendment 7 is rejected.

So if 2 and 5 are rejected then 6 is approved so the contrapositive creates an "or". Is that "or" inclusive or exclusive?

[Nikki Siclunov]

Hi Nicolle,

The "or" in question would indeed be inclusive. The original rule states, "If amendments 2 and 5 are rejected, amendment 6 is approved." So, the sufficient condition is the rejection of both amendments (2 and 5). By the contrapositive, if 6 is rejected, we must ensure that amendments 2 and 5 are not both rejected. In other words, either 2 must be approved, or else 5 must be approved, but of course it is entirely possible that 2 and 5 are both approved.

Hope this helps! Let me know.

Thanks.