The passage states which one of the following?

Andrew on May 25, 2018

Example 3.

I am confused on the logic in the correct answers. For B it says that no crimes has no laws. I thought no introduced a sufficient condition and a negation of the necessary condition (no crimes) would cause a negation of no laws so it would me (crimes --> no laws) but there is a no in front of laws which confuses me which is like a double negation of no laws (no crimes ---> no laws). Also I don't understand how you are diagramming C and E many statements are some statements. How are you diagramming them with sufficient and necessary conditions. Also the correct answer is D which I cant seem to wrap my head around -- its because of the atleast 1 terminology but you diagram some as sufficient and necessary which I didn't know you could do.

Replies

Michelle on May 28, 2018

Hey @AndrewDavis

Thanks for your question! I can see how this one would be confusing, because answer choices C through E do use the terms "some" and "many." The reason we diagram these as S&N statements is because the terms "some" and "many" are NOT used to describe the logical relationship between laws & crimes. They are simply used to note the presence and degree of each variable.

To give you an counterexample, imagine the statement "some societies with crimes have laws." This statement would be mapped as "C -s- L" because the "some" term is being used to explain the logical relationship between the two variables. Another way to think about it would be "A society with crimes SOMETIMES has laws."

The statement in the correct answer choice C is "A society that has some crimes has some laws." In this case, "some" is being used to indicate the presence of both crime and laws, but it does not denote the logical relationship between the two variables. In this case we could think of it as "A society with some crimes ALWAYS has some laws." Hence "if crimes than laws" or "C ==> L"

on August 3, 2019

How is the correct answer choice C Michelle , when the answer in the video is D, which is what I got as well? Also he diagrammed a Some statement C-> L, where I did it like in the quantifiers video C-s-L

Victoria on August 3, 2019

Hi @Lucas,

While answer choice D does use the word 'some,' it is not a 'some' statement as introduced in the quantifiers video. Answer choice D claims that "a society that has some crimes has some laws." In comparison, a 'some' statement, as discussed in the quantifiers video, is one that delineates the relationship between two variables i.e. some X are Y. Answer choice D uses the word 'some' to indicate that there is at least one crime and at least one law.

In this way, answer choice D is claiming that if the society has some (at least one) crimes, then it also has some (at least one) laws. Therefore, it is actually a S&N statement as opposed to a 'some' statement:

Some Crimes - > Some Laws OR C - > L

We can see that the above diagram directly mirrors the diagram drawn from the passage, making D the correct answer. Michelle wrote out the statement from answer choice D so her claim that the correct answer was C was clearly a typo.

Hope this helps! Please let us know if you have any further questions.