I'm a beginner learning about propositional logic and how to formalise sentences.
I'm currently working through the following sentences and translating them into logical statements.
- $p$ means “Emily is happy”
- $q$ means “Emily paints a picture”
- $r$ means “David is happy”
1. If Emily is happy then Emily paints a picture.
This is $p \implies q$.
2. If Emily is happy and paints a picture then David is not happy.
This is $[p ∧ q] \implies ¬r$.
3. David and Emily cannot both be happy.
I'm stuck on this last one.
I'm finding it difficult to understand how to go about formalising the last sentence. I was thinking it may include negating both $p$ and $r$ but the word "cannot" kinda throws me a bit. Any suggestions? Sorry if it's really obvious but I really am just starting out!