I'm very new to first-order logic. I've been working on some tasks below, and would appreciate if somone could check if I have understood and solved the questions correctly
Assume that $B$, $F$ and $K$ are relational symbols so that
- $Bx$ interpreted as "$x$ is a biologist
- $Fx$ interpreted as "$x$ is a philosopher"
- $Kxy$ interpreted as "$x$ knows $y$"
Assume that $a, b$ and $c$ are constant symbols which represents Aristoteles, Bolzano and Copernicus. Find first-order logic formulas for following sentences:
- Aristotle is both a biologist and a philosopher
- All biologists are philosophers
- No philosophers are biologists
- Aristoteles knows a philosopher
- Bolzano knows all philosophers
- Copernicus knows only biologists
Here are my answers:
There exists one $x$ so that Aristoteles is a $Gx$ and a $Fx$, written as $\exists$$x(Bx(a)$ $\land$ $Fx(a)$
For all $x$ if $x$ are $Bx$ so $x$ are $Fx$, written as $\forall$$x$$(Bx(x$) $\rightarrow$ $Fx(x)$
It's not that there is an $x$ such that $x$ are $Fx$ and $x$ are $Bx$, written as $\lnot$$\exists$$x(Fx(x) \land Bx(x)$
There exists one $x$ such that Aristoteles knows a $Fx$, written as $\exists$$x(Kxy(a, Fx)$
I would appreciate any help and please feel free to correct me if I've done something wrong.