Logic Problem with truth tables According to a truth table, if "p is false, and q is false" then "p implies q" is true. However, when studing inverses, we see that the inverse of a conditional statement may or may not be true.
For example, 
Statement:  If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
Inverse     If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides. (FALSE!)
Does this not contradict the truth table? 
In the inverse, p and q are both false; however, the inverse of the true statement is not true.
Please help!

$P\rightarrow Q$ is equivalent to saying that,


*

*If $P$ is true then $Q$ is true.


*If $Q$ is false then $P$ is false.

In other words, $P\rightarrow Q$ is equivalent to $\neg Q\rightarrow \neg P$.
In your example we take $$P:=\text{a quadrilateral is a rectangle}\\Q:=\text{a quadrilateral has two pairs of parallel sides}$$
It is not clear what you mean by inverse. However, if you want to mean converse then there is a mistake in your converse. It should be,

If a quadrilateral has doesn't have two pairs of parallel sides then it is not a rectangle.

And this is consistent with the truth table.
