What Must be True, Could Be True, Cannot Be True - Conditional Reasoning

tams2018tams2018 Member
in Logical Reasoning 727 karma

Hi!

I have been working in the core curriculum for some time and there is something that I am not quite clear about conditional reasoning and its inferences.

What I do know is that IF A, THEN B contraposes(is that a word?) to IF NOT B THEN NOT A. I know this must be true.

But what about IF NOT B THEN A? Is this a cannot be true or a could be true? Does this statement negate the original statement?

Help!

Comments

  • tams2018tams2018 Member
    727 karma

    Reference point: PT 23 S3 Q14 (Sufficient Assumption Problem Set 2)

    How can one translate answer choice D into lawgic?

    A: Proposed tax reduction package is adopted
    B: Library forced to discontinue its daily story hours
    C: Many parents greatly inconvenienced

    Sentence 1 A → B
    Sentence 2 B → C
    Sentence 3 /A

    Choice D= C→/A

    Is this correct? Help.

    Is the argument saying that the proposed tax reduction package will discontinue daily story hours and greatly inconvenience parents? So by D, its saying that that particular tax package won’t be adopted?

    Just trying to understand how it fits in the valid argument forms. Much appreciated.

  • Mellow_ZMellow_Z Alum Member
    1997 karma

    @tams2018 said:
    Hi!

    I have been working in the core curriculum for some time and there is something that I am not quite clear about conditional reasoning and its inferences.

    What I do know is that IF A, THEN B contraposes(is that a word?) to IF NOT B THEN NOT A. I know this must be true.

    But what about IF NOT B THEN A? Is this a cannot be true or a could be true? Does this statement negate the original statement?

    Help!

    Doesn't /B->A contradict what we said was the contrapositive (/B->/A)?

    If we conclude that if you are not a B then you must not be an A (only B's are A's), then if you aren't a B, you can't be an A.

    See this diagram for help visualizing : http://sketchtoy.com/68119077

  • Mellow_ZMellow_Z Alum Member
    1997 karma

    @tams2018 said:
    Reference point: PT 23 S3 Q14 (Sufficient Assumption Problem Set 2)

    Sentence 3 /A

    Choice D= C→/A

    Is this correct? Help.
    Is the argument saying that the proposed tax reduction package will discontinue daily story hours and greatly inconvenience parents? So by D, its saying that that particular tax package won’t be adopted?

    Just trying to understand how it fits in the valid argument forms. Much appreciated.

    So.

    If tax reduction is adopted --> discontinue DSH

    If discontinue DSH --> parents inconvenienced

    Combining the two statements :

    If tax reduction is adopted --> parents will be inconvenienced.

    The conclusion then states, that because of the given conditionals, the tax reduction will not be adopted. So we have a gap. What is this gap? The gap is that just because the parents are inconvenienced, we have no reason to believe that the tax reduction will be adopted.

    So in logic terms : if inconvenienced - > tax reduction not adopted

    In order to fill this gap, we look at the answer choices. D fills the gap.

    D says “If a tax reduction package inconveniences parents, then it will not be adopted this year.”

  • LSATcantwinLSATcantwin Alum Member Sage ⭐
    edited May 2017 13286 karma

    It may help to put this into words, easy ones.

    If you are a Dog, then you are Fluffy.

    D->F or /F -> /D

    You are asking /F -> D which says;

    If you are not Fluffy, then you are a Dog.

    Does that sound right?

    We just said that all Dogs MUST be Fluffy right? So if you are not Fluffy, how can you be a Dog? It simply can't be true based on what we know.
    who wants a non-fluffy dog?

  • tams2018tams2018 Member
    727 karma

    @Mellow_Z said:

    @tams2018 said:
    Reference point: PT 23 S3 Q14 (Sufficient Assumption Problem Set 2)

    Sentence 3 /A

    Choice D= C→/A

    Is this correct? Help.
    Is the argument saying that the proposed tax reduction package will discontinue daily story hours and greatly inconvenience parents? So by D, its saying that that particular tax package won’t be adopted?

    Just trying to understand how it fits in the valid argument forms. Much appreciated.

    So.

    If tax reduction is adopted --> discontinue DSH

    If discontinue DSH --> parents inconvenienced

    Combining the two statements :

    If tax reduction is adopted --> parents will be inconvenienced.

    The conclusion then states, that because of the given conditionals, the tax reduction will not be adopted. So we have a gap. What is this gap? The gap is that just because the parents are inconvenienced, we have no reason to believe that the tax reduction will be adopted.

    So in logic terms : if inconvenienced - > tax reduction not adopted

    In order to fill this gap, we look at the answer choices. D fills the gap.

    D says “If a tax reduction package inconveniences parents, then it will not be adopted this year.”

    OK! I guess I was confusing inference for filling the gap. Thank you for your explanation. I think i see the difference.

  • tams2018tams2018 Member
    727 karma

    @LSATcantwin said:
    It may help to put this into words, easy ones.

    If you are a Dog, then you are Fluffy.

    D->F or /F -> /D

    You are asking /F -> D which says;

    If you are not Fluffy, then you are a Dog.

    Does that sound right?

    We just said that all Dogs MUST be Fluffy right? So if you are not Fluffy, how can you be a Dog? It simply can't be true based on what we know.
    who wants a non-fluffy dog?

    Super helpful. Thank you!

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