# Thread: "only if" Conditional Statements

1. ## "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?

2. ## Re: "only if" Conditional Statements

Originally Posted by Bashyboy
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.