Natural Language to Formal Propositional Logic, "get neither"

Question

I've been working through a few translations and I found one I am not too sure as to the formatting of.

I believe the first part is right but in the second part where it says he will get neither, I am unsure if the correct format is to negate both symbols, or if there is another way?

The sentence is:

Johnny wants both a train and a bike for Christmas but he will get neither.

This is my current attempt of translation:

Jt = Johnny wants a train

Jb = Johnny wants a bike

$$(Jt\land Jb) \land \lnot(Jt \lor Jb)$$

Thank you

Answer 1

That doesn't work. Your sentence ends up saying:

Johnny wants both a train and a bike for Christmas but he $\color{red}{wants}$ neither.

You'll need to add some sentence variables that symbolize Johnny getting a train or bike.

So, say you have:

Wt = Johnny wants a train

Wb = Johnny wants a bike

Gt = Johnny gets a train

Gb = Johnny gets a bike

Then you can do:

$(Wt \land Wb) \land \neg (Gt \lor Gb)$

So: your idea was certainly correct ... but you just needed some additional sentences to capture the getting part