Let $x$ : A person
$h(x)$: $x$ is a historian and
$m(x)$: $x$ is a mathematician
No historians are non-mathematicians $\equiv$ There does not exist $x$ such that $x$ is historian and not a mathematician.$\equiv \sim \exists x(h(x)\wedge \sim m(x)) \equiv \forall x(\sim h(x) \vee m(x))$
- All historians are mathematicians $\equiv$ For all $x$, if $x$ is a historian, then it has to be a mathematician $\equiv \forall x(h(x)\rightarrow m(x))\equiv \forall x(\sim h(x) \vee m(x))$
- No historians are mathematicians $\equiv$ There does not exist $x$ such that $x$ is a historian and $x$ is a mathematician$\equiv \sim \exists x( h(x) \wedge m(x)) \equiv \forall x(\sim h(x) \vee \sim m(x))$
- Some historians are mathematicians $\equiv$ There exist some $x$ such that $x$ is a historian and also a mathematician$\equiv \exists x( h(x) \wedge m(x))$
- Some historians are not mathematicians $\equiv$ There exist some $x$ such that $x$ is a historian and also not a mathematician$\equiv \exists x( h(x) \wedge \sim m(x))$
$\therefore$ Option $1.$ is correct.