Is "If A then B" equal to "B if and only if A"?

Lafari@lemmy.world to No Stupid Questions@lemmy.world – 40 points –
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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

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

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…

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

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")?

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.

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?

Don't confuse this guy with ontological questions.

This is straight truth table level stuff.