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Math Help - if then statements

  1. #1
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    if then statements

    Say I have the statement: "None of the unnoticed things, met with at sea, are mermaids. "

    Lets say: M = set of mermaids
    N = set of things noticed

    If I wanted to convert this into an if then statment, would it be:

    M --> N (if it is a mermaid, then it is noticed)

    or

    N --> M (if it is noticed, then it is a mermaid)

    How do I know which is the correct if-then statement?

    Any help is appreciated!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DarK View Post
    Say I have the statement: "None of the unnoticed things, met with at sea, are mermaids. "

    Lets say: M = set of mermaids
    N = set of things noticed

    If I wanted to convert this into an if then statment, would it be:

    M --> N (if it is a mermaid, then it is noticed)

    or

    N --> M (if it is noticed, then it is a mermaid)

    How do I know which is the correct if-then statement?

    Any help is appreciated!
    think of the statement this way: if it is an unnoticed thing met at sea, then it is NOT a mermaid. (since no such thing is a mermaid)

    now what do you think the answer is?
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  3. #3
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    I think I got the statements in my first post mixed up with their contrapositives.

    Well, I have

    ~N -- > ~M
    (if it is unnoticed then it is not a mermaid)

    Again I'm a little confused, why can't I have it as:

    ~M --> ~ N
    (if it is not a mermaid then it is unnoticed)


    Thank you.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DarK View Post
    I think I got the statements in my first post mixed up with their contrapositives.

    Well, I have

    ~N -- > ~M
    (if it is unnoticed then it is not a mermaid)

    Again I'm a little confused, why can't I have it as:

    ~M --> ~ N
    (if it is not a mermaid then it is unnoticed)


    Thank you.
    your first implication is correct. and note that your second is its converse. it is not always true that the converse of a true implication is true. the converse is equivalent to N --> M, so you are saying that if it is noticed, it's a mermaid. clearly this isn't true, there are tons of things at sea that you notice that are not mermaids.
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