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Is "If A then B" equal to "B if and only if A"? (lemmy.world)
submitted 2 years ago by to c/nostupidquestions@lemmy.world
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[–] [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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  • [–] 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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  • [–] 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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