How can I write the following propositional logic in symbol format?

Question

Considering the proposition:

Neither person has cups, unless they have fridges

Considering:

person has cups -> p

have fridges -> q

How could I write this in the correct way?

Thanks

Answer 1

Using your notation: $P(x)$ is defined as "$x$ has cups", and $Q(x)$ is defined as "$x$ has fridges". Then you could write it like this: $$(\forall\,x)(P(x)\implies Q(x)).$$

Answer 2

Using $P(x)$ for "$x$ has cups" and $Q(x)$ for "$x$ has a fridge".

Adding to my comment, what would be the equivalent ways to write the sentence "No person has cups, unless they have a fridge", and also "No person that has cups has fridges"?

• "No person that has cups, does not have a fridge." $\neg\exists x~(P(x)\wedge \neg Q(x))$

• "Any person will have a fridge if they have cups." $\forall x~(P(x)\to Q(x))$

• "Any person will not have cups if they do not have a fridge." $\forall x~(\neg Q(x)\to \neg P(x))$