Confused on Conditional Statements Write these propositions using $p$ and $q$ and logical connectives (inclduing negations)
$p$: You drive over $65$ miles per hour.
$q$: You get a speeding ticket
You will get a speeding ticket if you drive over $65$ miles per hour
I got q implies p, but the book says $p$ implies $q$. Can someone explain this to me?
 A: The statement you will get a speeding ticket if you drive over 65 miles per hour is exactly the statement that $p$ implies $q$. It's actually phrased $q$ if $p$.
We cannot conclude that $q$ implies $p$. To give an explicit example, it might be the case that the speed limit is $40$ miles per hour, for instance. In this case, driving $65$ will give you a ticket (reminding ourselves that $p$ implies $q$), but getting a speeding ticket does not mean that you went $65$ (you might have gone $50$, for instance).
A: The statement says that if you drive over 65 then you will get a ticket. It is not necessarily true that if you get a ticket then you drive over 65. For example, suppose the speed limit is 60. If you get a ticket, you could have been driving only 63. That's still over the limit, but it isn't over 65.
Note that nowhere is it asserted that 65 is the speed limit.
It's also true that if you drive over 90 then you will get a ticket. But that doesn't means that if you get a ticket you were driving over 90.
