this post was submitted on 17 Jan 2024

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No Stupid Questions

nostupidquestions@lemmy.world

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Is "If A then B" equal to "B if and only if A"? (lemmy.world)

submitted 2 years ago by Lafari@lemmy.world to c/nostupidquestions@lemmy.world

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[–] Ep1cFac3pa1m@lemmy.world 22 points 2 years ago* (2 children)

If Nazi, then fascist = true

Fascist, if and only Nazi = not true

If car, then vehicle = true

Vehicle if and only if car = not true

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[–] Valmond@lemmy.mindoki.com 4 points 2 years ago (1 child)

I used the bananas are fruits analog but your one works well too!

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[–] Ep1cFac3pa1m@lemmy.world 7 points 2 years ago (1 child)

I just figured with Lemmy’s interest in politics it seemed like an obvious example. I threw in the car because I didn’t want to be that guy who makes everything about nazis…

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[–] Boinkage@lemmy.world 3 points 2 years ago (1 child)

Yeah careful with that, the logic example Nazis will be all over you if you don't mix it up some.

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[–] Ep1cFac3pa1m@lemmy.world 5 points 2 years ago

Not everything is about Nazis, Boinkage, geez…

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[–] Lafari@lemmy.world [S] 1 point 2 years ago (2 children)

If car, then vehicle = true

Car if and only if vehicle = true.

Is this correct?

Therefore "If A then B" = "A if and only if B" (or "If B then A" = "B if and only if A")?

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[–] zenharbinger@lemmy.world 6 points 2 years ago* (last edited 2 years ago)

B can still be true when a is false. iff means that b can only be true when a is true.

Also, the equivalent statement is.

vehicle if and only if car.

not

car only if vehicle

since a truck is a vehicle, the statement is false.

Somewhat wrong above:

A B a iff b

T T T

T F F

F T F

F F T

look online for truth tables.

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[–] Ep1cFac3pa1m@lemmy.world 1 point 2 years ago (1 child)

You’d have to firm up your definition of car and vehicle before you could decide that one. Does a hot wheels car count as a car? Does a vehicle have to be large enough to move people or freight?

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[–] zenharbinger@lemmy.world 7 points 2 years ago*

Don't confuse this guy with ontological questions.

This is straight truth table level stuff.

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