Explaining Logical Implication: "If P Then Q

[physicsuser]

Can someone try and explain it to me?
I cannot understand the meaning of implication ( if p then q) from truth table

p q p => q
t t t
t f f
f t t
f f t


so it is if p is true then q is true or if p is false then q is false?

then why if p is false and q is true, p implies q is true?

 

[mathman]

If p is false, q can be either true or false, therefore p=>q remains true. The only case where it is contradicted is p true and q false.

 

[matt grime]

This is one I have to explain a lot to new students. Here's the example that I find useful.

P is the statement 'n is divisible by 4'
Q is the statement 'n is even'

We can all agree that the proposition 'If P then Q ' is true, yep?

But n=6 is a case where P is false and Q is true.