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$$a) \quad \forall x\exists y(3x+4y=12)$$ $$b) \quad \exists x\forall y(3x+4y=12)$$

Am I correct in saying that a) is correct while b) is false?

Hirshy
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Heelloppp
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1 Answers1

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You are perfectly correct. The order of the quantifiers does matter (assuming $x$ and $y$ belong to $\mathbb{R}$).

Silvia Ghinassi
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GBQT
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  • can you explain in this specific context, why the order matters? – SeesSound Dec 11 '16 at 22:05
  • Well, in the first line, for any value of $x$, you must find $y$ so that $3x+4y=12$, which is obviously possible. However, in the second case, you need to find a value of $x$ for which the equation holds for any value of $y$, which is impossible. – GBQT Dec 12 '16 at 10:52