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Advanced Conditional Logic

ironofffironofff Member
in Logical Reasoning 70 karma

J.Y. Ping said:
(1) All bananas are made of atoms. [B–>A]
(2) All non-bananas are made of atoms. [/B–>A]
(1) and (2) are consistent with each other.
The contradiction (must be false statement) to (1) would be some bananas are not made of atoms. [B some /A]

HERE Where I AM CONFUSED!!!
But contradiction of all (B are A) is (not A not B) , hence (A is not B) is acceptable since we are failing sufficient only, but contrapositive of that is (B is not A) so we can say (B is not A) hence some bananas are not made of atoms. Please help someone.

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  • Sailor Moon LSATSailor Moon LSAT Member ⭐
    200 karma

    I think your post got a little but confusing with the :sunglasses: emoji which probably covers up some text.

    When you negate the first statement, you are saying You can be a banana and not be made of atoms (B some /A)

    The second statement negated is You can be a non-banana and also not be made of atoms (/B and /A).

    When you negate a logical statement, you want to deny the subsumption relationship and show that there is an intersection with something that before was thought not possible.

    Can you re-post the second half of your questions so I can try to help you out?

  • ironofffironofff Member
    70 karma

    But contradiction of all (B are A) is (not A not B) , hence (A is not B) is acceptable since we are failing sufficient only, but contrapositive of that is (B is not A) so we can say (B is not A) hence some bananas are not made of atoms. Please help someone.

  • ironofffironofff Member
    70 karma

    But contradiction of all (B are A) is (not A not B ) , hence (A is not B ) is acceptable since we are failing sufficient only, but contrapositive of that is (B is not A) so we can say (B is not A) hence some bananas are not made of atoms. Please help someone.

  • ironofffironofff Member
    70 karma

    I guess my mistake is that i took a contrapositive of a statement with existential quantifier (some, which I'm not allowed to do)

  • canihazJDcanihazJD Alum Member Sage ⭐
    edited May 2021 8491 karma

    @ironofff said:
    But contradiction of all (B are A) is (not A not B )

    That's a contrapositive, which is the logical equivalent, not a negation.

    A negation would be B some /A... despite your claim that all bananas are made of atoms, here is an example of at least one banana that is not made of atoms.

    From your first post it seems like you might be making an error here as well:

    hence (A is not B ) is acceptable since we are failing sufficient only, but contrapositive of that is (B is not A)

    You need to negate both when you swap them. So for example the contrapositive of A→B is /B→/A.

    Sounds like maybe you're getting your terms/mechanics mixed up?

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