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A necessarily accompanies B syllogism?

mkang89mkang89 Member
in Logical Reasoning 10 karma

My hunch tells me that this is supposed to be B-->A.
However, my buddy tells me that this is A-->B, which also sounds right.
I have another buddy who tells me that this is A<-->B because
(1) A accompanies B is B-->A
(2) Always is a sufficiency indicator, which means A-->B; ergo, A<-->B

In case you guys are wondering, this is PT51 Section 3 Number 20 Choice (A). This has nothing to do with the answer, but I still want to know :)

Could you guys help me with this?

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Comments

  • Logic GainzLogic Gainz Alum Member ⭐
    700 karma

    The lawgical implication stems from, "necessarily accompanies." This is the only indicator phrase in the whole sentence so that's where your focus should lie. Next, determine which variable that phrase is modifying. I.e., which of the two variables is that phrase talking about; A or B?

    Once you determine which variable that phrase is talking about, next decide what it means to necessarily accompany something else? I.e. are you on the left side of the conditional arrow (sufficient) or the right side of the arrow (necessary). I think only one of these is obvious...

    You should now have a good idea of which one of the above interpretations is right. If I were you, I'd lean heavily towards your hunch.

  • TheDeterminedCTheDeterminedC Member
    edited May 2019 1025 karma

    Clouds necessarily accompany rain.

    Rain -----> Clouds

    I think negating the statement helps intuitively understand it more:
    Clouds do not necessarily accompany rain (sometimes there is rain with no clouds).

    Rain <---s---> notClouds

    Rain <---s---> notClouds is logically equivalent to, not(Rain -----> Clouds). Both of these could be wrong. But the fact they both result in the same statement, when negated, leads me to think your hunch seems correct.

  • Possible_byfaithPossible_byfaith Member
    32 karma

    "A necessarily accompanies B"

    If I am B, what do you know about me fundamentally? I am accompanied by A. A depends on me, it can't help it. A is required to accompany me: so if B, then A (B-->A)

    If I am A, what do you know about me fundamentally? Nothing. I could accompany B, but I could also accompany C, or other good looking letters like Z. In other words, A (the necessary condition) is inactive when considered by itself.

    It took awhile for me to parse this out -- thanks so much for this brain teaser!

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