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Given the following structure:

$A = \{1,2,3\}$

$S^A = \{1,2\}$

$T^A = \{(1,2),(2,2),(2,3)\}$

$f^A(1) = 2$

$f^A(2) = 2$

$f^A(3) = 2$

can I say that the formula $∀xT(f(x),x)$ is satisfiable on the structure just because it is true for $x=3$ or should it be also true for $x = 1$ and $x = 2$?

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    \forall means "**for all**"... – 2017-01-02
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    So it is false. Thank you. – 2017-01-02
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    One more question: is $∀x∃y$ the same as $∃y∀x$? – 2017-01-02
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    No; "for all men there is a father" vs "there is a father of all men" ... – 2017-01-02

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