Contrapositive confusion - HELP!

keepgoing.keepgoing. Member
in Logical Reasoning 365 karma

if we have this statement
A --> B and C
Contrapose:
Not /B or /C --> /A
Simple enough

What if we find out only /C
then what remains?
Do we still get to run contrapositive?
What if this happens in a logic game Would (A-->B) still be the remaining rule?

help

Comments

  • cat.casacat.casa Member
    168 karma

    hey yeah you still run the contrapositive because the contrapositive is:
    /B or /C --> /A (like you said) which can be broken down into:
    /B ----> /A
    /C ---> /A
    so if you are given /C then it gives you /A
    I'm not sure what you mean about (A-->B) as a remaining rule. Your rule is (A --> B and C), nothing about this changes.

  • keepgoing.keepgoing. Member
    365 karma

    @"cat.casa" said:
    hey yeah you still run the contrapositive because the contrapositive is:
    /B or /C --> /A (like you said) which can be broken down into:
    /B ----> /A
    /C ---> /A
    so if you are given /C then it gives you /A
    I'm not sure what you mean about (A-->B) as a remaining rule. Your rule is (A --> B and C), nothing about this changes.

    Thank you for clearing that up. How about
    In the case A --> B or C
    and we find out C is satisfied - would that part of rule fall away and would still have A --> B remaining?

    especially in the context of logic game, this rule confused me^

  • cat.casacat.casa Member
    168 karma

    np. If you have A --> B or C and you are given C, then no you wouldn't have A ---> B remain as a rule bc A --> B or C doesn't necessarily translate into
    A --> B
    A --> C
    It CAN because "B or C" always implies "or both" but it doesn't necessarily have to so you can't presume it always does. I feel like you have to remember that only sufficient conditions (A) trigger anything. So if you are given a necessary condition (C), that doesn't do anything/change any rules/nothing falls away. The only time I can think of C making any difference given A --> B or C is in the case of the contrapositive where /B and /C ---> /A so if you don't have C, then you can't have A. Otherwise, C doesn't trigger anything.

  • AudaciousRedAudaciousRed Alum Member
    2689 karma

    If you had only /C, then no.. you couldn't have A. However... You could totally have B on its own. There's nothing saying that B couldn't survive off on its own, independent of /A and a /C.

  • keepgoing.keepgoing. Member
    365 karma

    @"cat.casa" said:
    np. If you have A --> B or C and you are given C, then no you wouldn't have A ---> B remain as a rule bc A --> B or C doesn't necessarily translate into
    A --> B
    A --> C
    It CAN because "B or C" always implies "or both" but it doesn't necessarily have to so you can't presume it always does. I feel like you have to remember that only sufficient conditions (A) trigger anything. So if you are given a necessary condition (C), that doesn't do anything/change any rules/nothing falls away. The only time I can think of C making any difference given A --> B or C is in the case of the contrapositive where /B and /C ---> /A so if you don't have C, then you can't have A. Otherwise, C doesn't trigger anything.

    just to follow up - if we have
    A --> B or C
    and we find out /C
    would we be able to conclude /A?

  • keepgoing.keepgoing. Member
    365 karma

    @"keepgoing." said:

    @"cat.casa" said:
    np. If you have A --> B or C and you are given C, then no you wouldn't have A ---> B remain as a rule bc A --> B or C doesn't necessarily translate into
    A --> B
    A --> C
    It CAN because "B or C" always implies "or both" but it doesn't necessarily have to so you can't presume it always does. I feel like you have to remember that only sufficient conditions (A) trigger anything. So if you are given a necessary condition (C), that doesn't do anything/change any rules/nothing falls away. The only time I can think of C making any difference given A --> B or C is in the case of the contrapositive where /B and /C ---> /A so if you don't have C, then you can't have A. Otherwise, C doesn't trigger anything.

    just to follow up - if we have
    A --> B or C
    and we find out /C
    would we be able to conclude /A?

    never mind - figured it out

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