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Not (A-->B) Question

sierra_km24sierra_km24 Member
in Logical Reasoning 73 karma

Hi all, quick question!
In the Harder MBT Questions unit, JY covers two questions that involve the negation of embedded conditionals. I'm a little confused on the negations, and was hoping someone had some insight.

PT 33 S1 Q11:

A --> B
NOT (A -->B) which becomes:
A some /B

PT 30 S2 Q20:

(A -->B) --> /C
C --> NOT (A-->B) which becomes:
C --> A and /B

Does anyone understand why the negation of (A-->B) in one problem resulted in a some statement, while in another problem resulted in an and statement? Thank you!

Comments

  • canihazJDcanihazJD Alum Member Sage ⭐
    edited June 2021 8485 karma

    A → /B necessarily includes A ←some→ /B, and therefore any individual instance of an A that is /B.

    A → /B negates A → B, but the minimum you need (or the standard negation for this test) is to show that in fact there is an instance of A that is not B, or A ←some→ /B

  • sierra_km24sierra_km24 Member
    73 karma

    @canihazJD said:
    A → /B necessarily includes A ←some→ /B, and therefore any individual instance of an A that is /B.

    A → /B negates A → B, but the minimum you need (or the standard negation for this test) is to show that in fact there is an instance of A that is not B, or A ←some→ /B

    Thank you for the response! I'm still a bit confused — why in one instance is there an "and" and in another, a "some"? I understand that "-->" inherently implies some, but what is the relationship between "and" and "some"?

  • canihazJDcanihazJD Alum Member Sage ⭐
    8485 karma

    I'd say they are operationally the same in this context. I don't have the question in front of me right now it was probably giving you something that basically said, "here is an instance where you have A and yet not B" in a less abstract example.

    So if I said:

    Asian people are good at math.
    canihazJD is Japanese and barely passed algebra (true story).

    I've given you:
    A → GM
    A←some→ /GM or "look at canihazJD who is A and /GM."

    You're only talking about one instance so all you can draw is a some relationship. If you expanded the set from just me sucking at math to a majority (or all) of a given set then that would be different.

    https://s8.favim.com/orig/72/racism-asian-math-stereotypes-Favim.com-675452.jpg

  • lovegamemakeslifefunlovegamemakeslifefun Member
    50 karma

    I see there are some discussion, i think your main issue is confusion, or how to deal with.

    Here is your problem, the first is negate the whole statement, the second is negate only part of the expression. To negate the whole statement, it is some. To negate just left (sufficient) right (necessary) portion, your proceed with negate AND, you will have /A OR /B. hopefully it is what you want.

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