truth table understanding When you look at the truth table for definition of implication there are three columns $A,B$ and $A \Rightarrow B$.
I have done my maths thinking of implication as noting in my mind 'whenever this is true, this (what follows) is true'
For example $x>1$ implies $x>0$ whenever the first inequality is true the second is. And i understand equivalence to mean whenever this is true what follows is true and visa versa in other words they are true on exactly the same set.
Going back to truth tables I dont exactly understand what the truth table I mentioned at the beginning is saying. 
If you had a statment $q$ is a member of the irrational numbers assigned this to $B$ and
$q^2= rt 2$ and assigned this to $A$, then without looking at the truth table I would know that $A$ implies $B$ so whenever $A$ is true $B$ is true.
I dont know how to apply this to the truth table and what exactly this table is telling me
 A: Your example, the implication from $x>1$ to $x>0$, is a very useful one provided you realize that this implication is a generally true fact, so that, for example, it can be used in calculations even if you don't (yet) know know the value of $x$.  In other words, the statement "$x>1$ implies $x>0$" is true for all real numbers $x$. 
For example, it is true when $x$ has the value $7$, in which case both of the inequalities $x>1$ and $x>0$ are true.
The implication is also true when $x=\frac12$, in which case $x>1$ is false and $x>0$ is true.
And the implication is true when $x=-42$, in which case both of the inequalities are false.
Summarizing this example, we have true implications with all combinations of true and false for the individual inequalities except when the assumption is true and the conclusion is false. If there were such a situation, then you'd certainly want the implication to be false, because a true assumption shouldn't lead, via a true implication, to a false conclusion.
So an implication ought to be considered false if the assumption is true and th conclusion false, and the implication ought to be considered true in all other cases.  Fortunately, that's exactly what the truth table for implication says.
