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.
- Neither apples nor bananas will give you the trophy
- 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?