PT1.S4.Q21 - a society in which there are many crimes

gioaragon95gioaragon95 Alum Member
edited April 2017 in Logical Reasoning 174 karma

I am Completely stumped on this question. I am not sure if I am correctly negating the statement nor understanding the some relationship here

Stimulus Statement: "No laws has No Crimes", Because no laws can be broken.

Makes sense to me. However, I am confused with the Negate necessary rule being applied here since we are given two "No" Indicators.

How I would do this: Laws - Crime

Why? Since we are given a double negative. However,

How this is correctly diagramed is: /Laws - /Crimes

Why? Can some one explain that to me?

Also What do we do when we are given double (negate necessary or negate Sufficient conditions)

Now the negation aspect of this question. Since we are given a no statement and this is a must be true then,

How I would negate this no Statement is: A society has some laws and some crime.

However this is not correct, this is what answer choice (C) says "A society that has many laws has many crimes"

But my Second question then is WHY IS (D) Correct?? " A society has some crimes and some laws"

Thank you so much to anyone that can help

Comments

  • beth.flandersbeth.flanders Alum Member
    212 karma

    I don't believe this to be a double negative situation. Here we have two separate thoughts. No laws is the first idea, the second idea no crimes. A negation as we know it or a contrapositive in LSAT splits two worlds in half, so a society with no laws versus a society with laws, then a society with no crimes versus a society with crimes.

    A double negative is when two negative elements of a sentence are pushed to make a positive element. For example: (1) You cannot not go to the store meaning you can go to the store or (2) There is not nothing to worry about; meaning there is something to worry about.

    Anyway, I put this into an If-then statement. If a society has no laws then a society has no crimes. /L -> /C; contrapositive C -> L which translated back to English would be If a society has crimes then a society has laws.

    Answer Choice
    (A) L->C; incorrect we cannot prove this according to the stimulus
    (B) /C->/L; incorrect; cannot prove this either.

    (A) and (B) are logical equivalents to each other but have the sufficient and necessary reversed from the stimulus.

    (C) many L -> many C; incorrect again this has the sufficient and necessary confused according to the stimulus.

    (D) some C -> some L; correct; this must be true according to the contrapositive and that the word some is vague which is easier to prove with some being equivalent to at least one. So if there is at least one crime then there must be at least one law.

    (E) many C -> many L; incorrect; The contrapositive from the stimulus states that If a society has crimes then a society has laws. The answer choice is stating a many relationship. So thinking in numbers, how many crimes must there be to how many laws are needed for those crimes. We can't prove this because we don't know from the stimulus. There could be many crimes for only one law, therefore it does not have to be true.

    I really struggled with answer choice (E) because of the some implying many rule; at first glance they both appeared to be the same answer until i started thinking numbers. Not sure if this was the correct approach. Perhaps they'll be some other feedback to clarify this.

  • gioaragon95gioaragon95 Alum Member
    edited April 2017 174 karma

    @"beth.flanders"

    Thank you so much Beth for the explanation. No I know how to read such a statement.

    I didn't know that there was quite a distinction with some and many. I just treated them as equal when seeing them.

    Many- 2-3
    Some- at least one

  • Mellow_ZMellow_Z Alum Member
    edited April 2017 1997 karma

    @gioaragon95 said:
    @"beth.flanders"

    Thank you so much Beth for the explanation. No I know how to read such a statement.

    I didn't know that there was quite a distinction with some and many. I just treated them as equal when seeing them.

    Many- 2-3
    Some- at least one

    I don't think you can actually quantify many. You can say definitely that MOST is >50%, but I don't think you will run into many (if any) instances where many is a quantifier that you need to use for subsets. Some others can likely chime in with better accuracy though.

  • beth.flandersbeth.flanders Alum Member
    212 karma

    @Mellow_Z said:

    @gioaragon95 said:
    @"beth.flanders"

    Thank you so much Beth for the explanation. No I know how to read such a statement.

    I didn't know that there was quite a distinction with some and many. I just treated them as equal when seeing them.

    Many- 2-3
    Some- at least one

    I don't think you can actually quantify many. You can say definitely that MOST is >50%, but I don't think you will run into many (if any) instances where many is a quantifier that you need to use for subsets. Some others can likely chime in with better accuracy though.

    I agree @Mellow_Z , I didn't think "many" could be a quantifier either, but it was the only thing I could think of that would distinguish answer choice D and E. I have seen some references where many is equivalent to several or few, meaning 2-3 but more so in mathematics versus logic. I wonder if this could be one of the differences between older and newer PT's. Hopefully some (or many) others will chime in :)

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