I'm trying to write the statement below into first order logic:
My dog Jude is drinking something from the bowl, and everything from the bowl contains germs except for potable water.
I'm using the following predicates Drinks(x,y), From(x,y), Bowl(x), ContainsGerm(x), PotableWater(x).
Not 100% sure about the correctness of the logic and quantifiers that I'm using here, so any advice or suggestion of alternative solution to be discussed is welcome:
$\small\exists x \exists y (({\operatorname{Drinks}(\operatorname{Jude},x)} ~\&~ {\operatorname{Bowl}(y)} ~\&~ {\operatorname{From}(x,y)} ~\&~ (\forall z ({\operatorname{From}(z, y)} ~\&~ {\lnot\operatorname{PotableWater}(z)}) \to \operatorname{ContainsGerm}(z)))$
Given the statement:
The logic representation of it is:
$$\exists y (\exists x (\text{Drinks}(\text{Jude},x) \land \text{Bowl}(y) \land \text{From}(x,y)) \\\land \forall z (\text{From}(z, y) (\land \lnot\text{PotableWater}(z)) →\text{ContainsGerm}(z))).$$