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"if and only if"

Don_DraperDon_Draper Alum Member

Does this phrase introduce the sufficient or necessary condition? Ex. Tina will enter the pool, if and only if Mike enters.

T->M
or
M->T

Thanks!

PS, I'm thinking it is the latter of the two.

Comments

  • akistotleakistotle Member 🍌🍌
    9382 karma

    This lesson talks about "if and only if":

    Advanced: Bi-Conditionals
    https://7sage.com/lesson/advanced-bi-conditionals/

    It's not "T->M or M->T" but it is "T->M and M->T"

  • Don_DraperDon_Draper Alum Member
    88 karma

    @akistotle said:
    This lesson talks about "if and only if":

    Advanced: Bi-Conditionals
    https://7sage.com/lesson/advanced-bi-conditionals/

    It's not "T->M or M->T" but it is "T->M and M->T"

    Thanks, I haven't gotten there in the CC.

  • Trust But VerifyTrust But Verify Alum Member
    432 karma

    The conditional lessons are crucial. You'll mentally enjoy.

  • Seeking PerfectionSeeking Perfection Alum Member
    4428 karma

    @teetime64 said:
    Does this phrase introduce the sufficient or necessary condition? Ex. Tina will enter the pool, if and only if Mike enters.

    T->M
    or
    M->T

    Thanks!

    PS, I'm thinking it is the latter of the two.

    As @akistotle noted it's both.
    The if gives us
    M-->T
    If Mike enters then Tina will enter.

    The only if gives us
    T-->M
    Only if Mike enters will Tina enter. So if Tina enters Mike must have entered.

    And also as you can probably see, both
    ¬T --> ¬M
    from M-->T

    and
    ¬M -->¬T
    from T-->M

    Biconditionals are powerful things!

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