# Thread: How would one make this statement false?

1. ## How would one make this statement false?

[ $\forall$x $\in$D, A(x)] $\Rightarrow$ [ $\exists$x $\in$D, A(x)]

If you were to define your own domain D and predicate A, how would you make this statement false?

My interpretation of this is:
Let D be the set of humans and A(x): "x is alive".
If all humans are alive, then there is a human that is alive.

I have no idea how to make this statement false.

2. ## Re: How would one make this statement false?

If a statement is true for all objects, then there exists an object for which it is true. This holds as long as there exists at least one object. If there are no objects, then the conclusion of the implication cannot be true regardless of the statement.

3. ## Re: How would one make this statement false?

Let $D$ be the set of all humans who are 100 feet tall.