Thread: ∀n(3n ≤ 4n) Domain: all integers ??

There is a problem in my Discrete Math book concerning Universal Quantification:

∀n(3n ≤ 4n)
Domain: all integers
True or False

I answered false because of negative integers. The answer in the back of the book says it's true. Is that a mistake on the books part or am I missing something here?

Originally Posted by brighamandrew

There is a problem in my Discrete Math book concerning Universal Quantification:

∀n(3n ≤ 4n)
Domain: all integers
True or False

I answered false because of negative integers. The answer in the back of the book says it's true. Is that a mistake on the books part or am I missing something here?

As written, the statement is false.
If the domain were all natural numbers then it would be true.
So check the wording again in the textbook.

Originally Posted by Plato

As written, the statement is false.
If the domain were all natural numbers then it would be true.
So check the wording again in the textbook.

It's definitely all integers. It must be a typo. Thank you for your help.