I am not able to understand these lines from deductive reasoning " Conclusion can only be false if atleast one of the premises is also false. If both premises are true, then conclusion is also true. We will say that argument is valid if the premise cannot be all true without the conclusion being true as well.  "
I am not able to understand meaning of these lines in textbook. Can anyone clarify ?
Thank You
 A: *

*You know contraposition. The contrapositive of " if A then B " is " if B is false, then A is false", or, more precisely, " if not-B, then not-A". 

*A proposition and its contrapositive sentence are equivalent, they mean exactly the same thing. 

*The definition of deductive validity says that a reasoning is valid just in case : 

if all the premisses are true, then ( necessarily)  the conclusion is true.



*

*By contrapositon, it can also be phrased : 



if the conclusion is false ( i.e. not true) , then not all the premises are true (
  meaning that at least one premise is false).

So 
(1) if I know that a reasoning is valid 
(2) and that its conclusion is actually false 
(2) then , I can claim with certainty that at least one of its premises is false ( one or more, possibly all). 
A: An argument is called valid if its premises imply its conclusions. In other words, if a valid argument's premises are true, its conclusion is true. (A valid argument with true premises is called sound.) We can restate this equivalently with the contrapositive: if a valid argument's conclusion is false, at least one of its premises is false. 
A: I suspect that you might be especially confused with the tongue-twisting phrase “argument is valid if the premise cannot be all true without the conclusion being true as well”.
Perhaps things can be illustrated by an example. Suppose I tell you, “You’ll never see me in the park on a Sunday”. This just means “If it’s a Sunday, you won’t see me in the park.” Now, suppose it is a Monday and we run into each other at the park. Have I broken my promise/claim? No. Although the conclusion is false (i.e. you did catch me in the park), the premises weren’t fulfilled: it’s a Monday, not a Sunday. So I haven’t broken my promise/claim.
The only way you could invalidate my claim is if you find me at the park on a Sunday. In other words, you can only invalidate my claim if the premises are true (i.e. it’s a Sunday), but the conclusion is false (i.e. you did see me in the park). This is what is meant when we say that an argument/claim is valid “if the premise cannot be all true without the conclusion being true as well”. It means we cannot have the following: the premises all true, but the conclusion false. My claim that “You’ll never see me in the park on a Sunday” will be valid so long as whenever it’s a Sunday (i.e. the premise is true) you don’t see me at the park (i.e. the conclusion is also true). However, I could be at the park on any other day of the week: that doesn’t invalidate my claim.
