"if and only if"

Don_Draper

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.

akistotle

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_Draper

@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 Verify

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

Seeking Perfection

@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!