# If all the premises are true and the conclusion is false, is it possible for the argument to be logically valid? [duplicate]

Where an argument is logically valid "if and only if it is not possible for the premises to be true and the conclusion false."

Are there any examples of a logically valid argument where the premises are all true, but the conclusion is false? Or is such an argument automatically logically invalid?

Is there any way for the statement "If all the premises of an argument are true and the conclusion is false, the argument is logically invalid" to be false?

## 1 Answer

The definition of an argument being (logically) valid is :

whenever the premises are true, also the conclusion must be true

or, alternatively, (as in you post) :

it is not possible for the premises to be true and the conclusion false.

If we write the last definition in a logically more perspicuous form, it says :

if (all premises are true), then (the conclusion is false).

This is : "if P, then Q"; the negation of this formula is : "P and not Q, which is :

(all premises are true) and (the conclusion is false).

This means that the condition that "all the premises are true and the conclusion is false" is the negation of the condition defining valid.

In conclusion :

if all premises are true and the conclusion is false, the argument is not valid.