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A > Either B or C. and then No C... What Must Be True?

PositivePositive Alum Member
edited March 2018 in Logical Reasoning 426 karma

Problem: PT 2 - S2 - #13

To simplify,
If A then, either B or C. And we were given No C. What Must Be True?

  1. No A
  2. or Can we still say A > B despite no C?

I am a bit confused... Any helps will be very much appreciated! Thank you in advance!!!!! : )

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Comments

  • NotMyNameNotMyName Alum Member Sage ⭐
    5320 karma

    We need to distinguish conditional statements from the conditions provided and their results. Conditional statements provide a map of meaning which we can use to determine inferences if we are given relevant conditions. No matter what conditions are provided, the maps still hold.

    So in the case of "If A then either B or C" where we are given /C, we can conclude /A and that's it. However the map still holds: it is still true that if we have A then we either have B or C. But that hypothetical is no longer helpful since we are told that we have /C.

    Make sense?

  • PositivePositive Alum Member
    426 karma

    @jkatz1488 Thank you very much for your detailed comments! It was very helpful! : )

  • _____Wale_____Wale Alum Member
    74 karma

    Retail stores experience decrease in revenue ==> (attitude towards extravagant gift-giving changed => prices risen beyond the level most people can afford)

    Attitude towards extravagant gift-giving changed => something to celebrate

    prices risen beyond the level most people can afford => salaries haven't kept up with rising prices during the past year.

    Given the premise, "if salaries have kept up with rising prices during the past year" what must be true?

    Since this is just a negation of the necessary condition in the last sentence of the stimulus, you can conclude the negation of the sufficient condition i.e. "prices have not risen beyond the level most people can afford" (AC: C)

    They're basically asking us for the contrapositive of the last statement.

  • goingfor99thgoingfor99th Free Trial Member
    edited March 2018 3072 karma

    If A then B/C.
    ~A.
    Therefore, we can still have B and C.

    If we are given no C, we need to have B in order to have A.

    A -> B
    ~B -> ~A

  • brigittebrigitte Free Trial Member
    432 karma

    @jkatz1488 said:
    We need to distinguish conditional statements from the conditions provided and their results. Conditional statements provide a map of meaning which we can use to determine inferences if we are given relevant conditions. No matter what conditions are provided, the maps still hold.

    So in the case of "If A then either B or C" where we are given /C, we can conclude /A and that's it. However the map still holds: it is still true that if we have A then we either have B or C. But that hypothetical is no longer helpful since we are told that we have /C.

    Make sense?

    How does /C allow you to conclude /A? A -> B or C means you can have /C but still have A as long as you have B. To conclude that we have not A we need to know that we have /B and /C.

  • NotMyNameNotMyName Alum Member Sage ⭐
    edited March 2018 5320 karma

    @anonclsstudent Ah! Thank you for checking that! My bad. Ugh hate making careless mistakes... especially public ones.

    We have:

    A > B/C
    B>D
    C>E
    /E

    /C (retail prices haven't risen beyond the level...)

    That's the correct logic.

    The essence of my answer holds: A>B still stands except it's a hypothetical and unhelpful in a MBT.

    Sorry for the confusion.

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