# How would one make this statement false?

• Sep 30th 2013, 07:58 PM
Turgus
How would one make this statement false?
[$\displaystyle \forall$x$\displaystyle \in$D, A(x)] $\displaystyle \Rightarrow$ [$\displaystyle \exists$x$\displaystyle \in$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.
• Oct 1st 2013, 04:30 AM
emakarov
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.
• Oct 1st 2013, 06:08 AM
SlipEternal
Re: How would one make this statement false?
Let $\displaystyle D$ be the set of all humans who are 100 feet tall.