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A -> B

  1. Nov 3, 2007 #1
    i don't understand why this notation is the same thing as

    "A only if B"

    to me "A only if B" reads that A is a consequence of B but of course it actually means the reverse.

    same thing with A<->B being stated as

    "A if and only if B"

    to me this reads that again A is a consequence of B and is only true when B is true. I don't understand how it tells anything about B or how you read the reverse implication from it, as far as english goes.

    woops i meant this for general math, wasn't looking.
     
  2. jcsd
  3. Nov 3, 2007 #2

    Hurkyl

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    If we know that "A only if B", then which if these following cases are possible?

    A is true and B is true.
    A is true and B is false.
    A is false and B is true.
    A is false and B is false.
     
  4. Nov 3, 2007 #3
    if i were reading and interpreting the way i'm inclined to, back wards that is, all but the second. the correct answer is of course all but the third.

    the truth table i would write for the statement "A only if B" is

    B is true and A is true.
    B is true and A is false.
    B is false and A is true.
    B is false and A is false.

    now i would say all but the third.
     
  5. Nov 3, 2007 #4

    Hurkyl

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    You are interpreting it correctly... "A only if B" means the same thing as "if A then B", and the case it excludes is "A is true and B is false".

    Maybe you are confusing "A only if B" with "A if B"?
     
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