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Math Help - If A happens, then B happens...

  1. #1
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    If A happens, then B happens...

    Please help me:

    In the following case, I can't decide if it's valid or invalid because I don't know if B HAS to happen if A happens. Can someone clarify?

    "If A happens, then B happens.
    A does not happen.
    Therefore, B does not happen.
    VALID/INVALID, WHY?"
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Let A be an apple growing
    Let B a fruit growing


    If A then B:
    if an apple has grown then a fruit has grown

    but if an apple hasn't grown then a fruit still could've grown i.e. like an orange

    therefore invalid
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by pleasehelpme12345 View Post
    Please help me:

    In the following case, I can't decide if it's valid or invalid because I don't know if B HAS to happen if A happens. Can someone clarify?

    "If A happens, then B happens.
    A does not happen.
    Therefore, B does not happen.
    VALID/INVALID, WHY?"
    If a statement is true, then its contrapositive is true. A statement and its contrapositive are logically equivalent.

    "If A, then B is TRUE", then the contrapositive would be "If not B is TRUE, then not A is TRUE"

    Using your statements:

    (1) If A, then B
    (2) Not A
    (3) Therefore, not B

    Your second statement is not the contrapositive of the first statement. It is the inverse of the first statement. Therefore, not logically equivalent; therefore INVALID conclusion.

    A valid argument would have been:

    (1) If A, then B
    (2) Not B
    (3) Therefore, not A



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