In Artificial intelligence, I saw the following question and answer in website.
Question:
Politicians can fool some people all of the time, and they can fool all people some of the time, but they can’t fool all of the people all of the time. $\newcommand{Politician}{\operatorname{Politician}}\newcommand{Person}{\operatorname{Person}}\newcommand{Fool}{\operatorname{Fool}}\newcommand{Time}{\operatorname{Time}}$
Answer:
Let $\Fool(x,y,t)$ mean that $x$ can fool $y$ at time $t$.
$\begin{align} \forall x (\Politician(x) &\rightarrow\\ &(\exists y \Person(y) \rightarrow (\forall t \Time(t) \rightarrow \Fool(x,y,t))) \land\\ &(\exists t \Time(t) \rightarrow (\forall y \Person(y) \rightarrow \Fool(x,y,t)) \land \\ &(\exists t,y \Time(t) \land \Person(y) \rightarrow \lnot\Fool(x,y,t)) \end{align}$
Could I write it in the following way. Is that correct?
My Solution:
$ (\forall x\, \exists y\, \forall t\, (\Politician(x) \land \Person(y) \land \Fool(x,y,t)) \land\\ (\forall x\, \forall y\, \exists t\, (\Politician(x) \land \Person(y) \land \Fool(x,y,t)) \land\\ \lnot(\forall x\, \forall y\, \forall t\, (\Politician(x) \land \Person(y) \land \Fool(x,y,t))$