Introduction to Logic

Exercise 2.6 - Natural Language

Consider a propositional language with three propositional constants - mushroom, purple, and poisonous - each indicating the property suggested by its spelling. Using these propositional constants, encode the following English sentences as Propositional Logic sentences. Use ~ for ¬; use | for ∨; use & for ∧; use => for ⇒; and use <=> for ⇔ when entering compound sentences.

All purple mushrooms are poisonous.
A mushroom is poisonous only if it is purple.
A mushroom is not poisonous unless it is purple. 
No purple mushroom is poisonous.