Regarding numerically definite quantification in predicate logic, I am struggling to formulate the following sentence due to it's complexity:
"Ada likes exactly two strong people, at least one of whom is old"
(Where $a$: Ada, $Lxy$: $x$ likes $y$, $Sx$: $x$ is strong, $Ox$: $x$ is old)
I have translated it to:
$\exists x\,\exists y\,(((Sx\land Sy)\land x\neq y)\land ∀z\,(Sz\to z=x\lor z=y)\land \exists x\,\exists y\,(Ox\lor Oy)\land (Lax\land Lay)$
I am fairly confident that my translation of 'There are at exactly two strong people' is correct: $\exists x\,\exists y\,(((Sx\land Sy)\land x\neq y)\land ∀z\,(Sz\to z=x\lor z=y))$.
However I am questioning whether my sentence is ordered correctly so that it conveys the fact that one of the strong people is old but that Ada likes both of the strong people.
I would appreciate any help clarify this, thank you.
(I am beginner in logic so please don't judge my attempt too harshly!)