/sci/ - Science & Math

>>9186628
Statement
>All phones in this room are turned off
"Converse"
>Everything in this room which is off is also a phone
"Inverse"
>All phones in this room are on
"Contrapositive"
>Nothing in this room which is on is also a phone

Now I'm sure you're irked that in the particular case where there are no phones in the room, what you will intuitively interpret as the statement, its converse, inverse and contrapositive, don't have their usual truth values. Namely, the statement and its inverse have the same "truth". But perhaps the statement can be rephrased, and with more precise language we can get to the bottom of this.

Statement
>If there is a phone in this room, it is certainly off.
Converse
>If something is certainly off, it is a phone in this room.
Inverse
>If there is a phone in this room, its power state is unknown.
Contrapositive
>If something's power state is unknown, it is not a phone in this room.

Everything is now working as intended. The issue was found: the opposite of "off" isn't "on". It's "might be off". And "might be off" [math]\implies[/math] "might be on" [math]\implies[/math] "power state is unknown".

>>9065534
Dawkins: Christianity is bullshit.
SJW: Haha yeah, get 'em!
Dawkins: Islam is bullshit.
SJW: H-hold on a second.

>>8993270