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.
A mushroom is poisonous only if it is purple.
b.
A mushroom is not poisonous unless it is purple.
c.
No purple mushroom is poisonous.
d.
mushroom & purple => poisonous
mushroom & poisonous => purple
mushroom & ~purple => ~poisonous
mushroom & purple => ~poisonous
a)(purple & mushrooms)<=> poisonous
b) (mushroom & poisonous ) => purple
c) (mushroom => ~poisonous) | purple
d) ( purple & mushroom ) => poisonous
sir please send me correct answer for verification
To encode the given English sentences as propositional logic sentences using the provided propositional constants, we can assign a variable to each sentence and represent the logical relationships using logical operators.
For the given propositional constants:
- mushroom: M
- purple: P
- poisonous: Q
a. All purple mushrooms are poisonous.
This sentence can be represented by the propositional logic sentence:
P & M => Q
b. A mushroom is poisonous only if it is purple.
This sentence can be represented by the propositional logic sentence:
Q => (P & M)
c. A mushroom is not poisonous unless it is purple.
This sentence can be represented by the propositional logic sentence:
~Q => (P & M)
d. No purple mushroom is poisonous.
This sentence can be represented by the propositional logic sentence:
~(P & M) => ~Q
In the propositional logic sentences above:
- & represents the logical AND operator.
- => represents the logical implication operator.
- | represents the logical OR operator.
- ~ represents the logical NOT operator.
These representations capture the logical relationships described in the English sentences using the given propositional constants.