Unless the residents of Glen Hills band together, the proposal to rezone that city will be approved. If it is the cit...
JROJune 7, 2019
Question #7
Hello. The first sentence on question #27 states: Unless the residents of Glen Hills band together, the proposal to rezone that city will be approved. On the explanation video, that statement is diagrammed as:
Not band together---> Proposal approved
And then of course reversing and negating the above in order to arrive at its contrapositive.
Is that not wrong since " 'unless' introduces a necessary condition," which would mean that "not band together" should go after the arrow since the diagram is supposed to reflect the rule "S ----> N" and not "N --->S" ? This is all very misleading, unless of course I am just completely mistaken, which is probably what it is.
Should the proper diagram not be:
proposal NOT approved ---> Band together
Band Not together ---> proposal approved (contrapositive)
It seems that what LMAX wrote down as the contrapositive should have come first and then vice versa.
The rule, along, with the example that LMAX gave us concerning "unless" statements is different than what we learned in the Sufficient and Necessary Conditions Video in the 1 hour, 30 minutes and 32 seconds mark:
"Unless" statements
The Rule:
Step 1: "Unless" introduces a necessary condition so the part of the sentence that follows "unless" will be the necessary condition.
Step 2: Negate the other part of the sentence and make it the sufficient condition.
LMAX's example: A person cannot win the lottery "unless" she buys a ticket.
WL ---> BT
not buy ticket ---> not win lottery (contrapositive)
Where did I go wrong?
Replies
Create a free account to read and
take part in forum discussions.
Unless the residents of Glen Hills band together, the proposal to rezone that city will be approved.
Based on the rules, "unless" introduces the necessary condition. The other part of the sentence is negated and put in the sufficient condition.
Proposal not approved - >Band Together
Not Band Together - >Proposal approved
These two statements are logically equivalent because they're each other's contrapositive. Thus, the explanation video's diagram is correct.
Does that make sense? Let us know if you have any questions!
ryanmeguiarNovember 21, 2019
@Ravi I understand what you're saying about the video technically being right because the statements "not approved -> band together and not band together -> approved" being logical equivalents however it is pretty confusing as a student to watch the video explanation start off with the contrapositive version. Unless introduced the necessary statement " band together" the sufficient is negated and written as "not approved".
Honestly I got a little frustrated watching the video because as soon as the instructor diagramed the sentence in the contrapositive version I personally felt like I had no idea in what I was doing despite the fact that I had it right. It made me think maybe I've completely read the problem wrong. Kind of discouraging.
