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Math Help - "only if" Conditional Statements

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    "only if" Conditional Statements

    Hello,

    I am having trouble seeing how "q only if p" statements transform to "If q, then p." When I read "q only if p" I understand it as q can only happen (occur) if p happens (occurs) first; that is, if p occurs, then q occurs, which simplifies to, "If p, then q." Can someone help me with this predicament?
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    Re: "only if" Conditional Statements

    Quote Originally Posted by Bashyboy View Post
    I am having trouble seeing how "q only if p" statements transform to "If q, then p." When I read "q only if p" I understand it as q can only happen (occur) if p happens (occurs) first; that is, if p occurs, then q occurs, which simplifies to, "If p, then q." Can someone help me with this predicament?
    I am changing notation on you.

    \text{If }P\text{ then }Q,~P\to Q is false in only one case and that is when P \equiv T\;\& \;Q \equiv F.

    Now think about that phrase "is false in only one case" as compared to only if

    \text{If }P\text{ then }Q,~P\to Q must be equivalent to Q\text{ only if }P.

    There are many, many ways to say the same thing.

    Please, comment on this if it does not help you.
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