Unmentioned possibility in bi-conditional stimulus

JCEM2021

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"?

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canihazJD

@"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

JCEM2021

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