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Unmentioned possibility in bi-conditional stimulus

JCEM2021JCEM2021 Core Member
edited March 2021 in Logical Reasoning 22 karma

In the lesson on bi-conditionals (Lesson 7 of 18 in Advanced Logic), we are told that "Alan attends the meeting only if Chris attends the meeting" is expressed as "A>C." I get that. But don't we need another expression that says in effect, "otherwise [or else], Alan does not attend"?

Admin Note: https://7sage.com/lesson/advanced-bi-conditionals/

Comments

  • canihazJDcanihazJD Alum Member Sage
    edited February 2021 8491 karma

    @"liz.morrill" said:
    In the lesson on bi-conditionals (Lesson 7 of 18 in Advanced Logic), we are told that "Alan attends the meeting only if Chris attends the meeting" is expressed as "A>C." I get that.

    It's been a while since I've seen that lesson but what you describe "Alan attends the meeting only if Chris attends the meeting" isn't a bi-conditional. You just get:

    A → C :: If A then C

    But don't we need another expression that says in effect, "otherwise [or else], Alan does not attend"?

    That's just the contrapositive of the previous statement, which is the implied logical equivalent :

    /C → /A :: If not C ("otherwise") then not A.

    A bi-conditional would be A if and only if C, or A ↔ C. Combining:

    A only if C :: A → C

    and

    A if C :: C → A

    giving you A ↔ C

  • JCEM2021JCEM2021 Core Member
    22 karma

    Ha. So true. Thank you for pointing that out.

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