Representing sentences as propositional logic statements

Question

I'm currently studying logical propositions through distance education for a college course and I'd like some assistance and critique on translating simple sentences into propositional logic statements.

These statements are based around trying to reach the trophy by obtaining different fruit.

1. Neither apples nor bananas will give you the trophy
2. Strawberries will give you the trophy but grapes will make you sick

The first one had me quite confused because of the nor word. I'm confused as to whether I should join them with an and or an or because they don't seem dependent on each other and it doesn't say anything about what happens when they are both true. My current thinking is this $\sim apples \land \sim bananas$

For the second one, I understand the strawberries part but I'm struggling with trying to represent the grapes part. I know that it will always be false. I started off with $strawberries \lor (grapes \land 0) $ but I'm not sure if this is correct. I decided to and the grapes with a 0 to make it always false but should I be using $\sim grapes$ instead?

Answer 1

Neither x nor y simply means "Not x and not y" when thinking about real life situations. So when writing this down logically, this will simply become $\neg x \wedge \neg y$, as it would be in any other situation (I am neither 20 nor 21 years old is the same as "I am not 20 years old and I am not 21 years old".

For the second, $grapes\wedge 0$ is just the same as $0$, so that's not what you want. Instead, take $\neg grapes$