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!

Ok, so you know that $p \rightarrow q$ is true when $p$ and $q$ are false. The inverse $\neg p \rightarrow \neg q$ is also true when $p$ and $q$ are both false. 
Your confusion seems to be that you are conflating the above situation with a different claim: $(p\rightarrow q) \rightarrow (q\rightarrow p)$. Notice that this is false in general, but given that $p$ and $q$ are both false, it is true.
So in your example it is indeed true that if a quadrilateral is a rectangle there are parallel sides, and indeed the converse of this statement is false, so we don't have $(p\rightarrow q) \rightarrow (q\rightarrow p)$ where $p$ is "is a rectangle" and $q$ is "has parallel sides". However, if I am given a quadrilateral which is neither a rectangle, nor has parallel sides, both the conditionals are true, so in this situation they imply one another (as a true thing is implied by everything).
