Proving a quantified statement wrong The domain is the natural numbers set.
I want to prove this statement wrong, however, I'm not sure how should I go about that since, theoretically, I would have to go through all y values in order to find at least one that would be fit for every single x value. Can anyone give me a tip?
Here's the statement:
∃y∀x(2x - y = 0)
Asserting that$$\exists y\forall x(2x-y)=0$$is false is the same thing as asserting that$$\forall y\exists x(2x-y\ne0)$$is true. And it is indeed true: for any $y$, just take $x=y$ if $y\ne0$ and $x=1$ if $y=0$.
Asserting that$$\exists y\forall x(2x-y)=0$$is false is the same thing as asserting that$$\forall y\exists x(2x-y\ne0)$$is true. And it is indeed true: for any $y$, just take $x=y$ if $y\ne0$ and $x=1$ if $y=0$.