I have homework that asks State whether the following quantified formulae are true over the natural numbers 1. x y z [ x+1 = y ² +z ² ] 2. x y z [(x > y) (x ³ < y ³ +z ³ )]

I missed class one day but we discussed looking at this as a game between two players. The Universal and Existential players. The existentail player seeks to satisfy the outcome and the universal seeks to falsify. So looking at the 1st example above, the universal player goes first and is looking to find a value of x that will make the formula false?

Clearly if x = 2 then 2+1=3 and there are no values for y or z that can make this statement true. So would I then say that the formula is false over the natural numbers?

Looking for conformation on this to be sure I understand the process. An example would also be helpful as I'm a little confused by the examples that have the same player going two times in a row. I'm sure I'm just reading too much into it, but clarification would be appreciated.