Why a false statement can imply anything? According to the truth table,
If $P$ is false,then $P-&gt;Q$ is true.

if pigs fly, then $1+1=3$. Why is this implication true? How do you prove it?
Suppose you say that "If it's raining, then the ground is wet."  

Then someone responds: "But the ground is dry."  

Your response would be:  "So what?  It's not raining, so my statement is still valid!"
It's a convention, so you can say eg. for all $x\in\mathbb R$ the following is true:

$$x\geq0\Longrightarrow x^2\geq0$$

This would be false if you didn't define it that way, because $-1&lt;0$ even though $(-1)^2&gt;0$.