I am studying for my exams and I am facing some issues with the "at least" statement in propositional logic.
Mary wants to mix a magic potion. Here is the recipe.
(1): You need at least one of the following ingredients: spider legs, eyes of a toad, magic mushrooms.
(2): If you are using magic mushrooms, then you can not use the other two ingredients.
(3): If you don't use magic mushrooms and spider legs, then you aren't allowed to use eyes of a toad.
- $s =$ spider legs
- $m =$ magic mushrooms
- $e =$ eyes of a toad
My solution would be something like this, but I am not sure about the first one. Feedback would be nice
- (1) $= (m \vee e) \wedge (m \vee s) \wedge (e \vee s)$
- (2) $= (\neg s \wedge \neg e) \rightarrow m$
- (3) $= (\neg m \wedge \neg s) \rightarrow (\neg e)$
Is the first equation correct?