Proving a quantified statement wrong

Question

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)

@wintersun: Can you write down the negation of that statement? — Brian M. Scott, Dec 18 '20 at 18:11

score 0 · Accepted Answer · answered Dec 18 '20 at 18:13

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 $y=0$.

answered Dec 18 '20 at 18:13

José Carlos Santos

427,504

Thank you, this one made things clear for me. – wintersun Dec 18 '20 at 18:58
I'm glad I could help. – José Carlos Santos Dec 18 '20 at 18:59

Proving a quantified statement wrong

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