a. For the sentence B ∨ C, there are two models: {B, C} and {B}.
b. For the sentence ¬A ∨ ¬B ∨ ¬C ∨ ¬D, there are eight models: {A, B, C, D}, {A, C, D}, {A, B, D}, {A, B, C}, {A, D}, {A, C}, {A, B} and {A}.
c. For the sentence (A ⇒ B) ∧ A ∧ ¬B ∧ C ∧ D, there is one model: {A, C, D}. This is because the sentence implies that A must be true and B must be false and that C and D must both be true in order for the sentence to be valid. As there are only four propositions, and A, C, and D must all be true and B must be false, there is only one model that satisfies the sentence.
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Complete question:
Consider a vocabulary with only four propositions, A, B, C, and D. How many models are there for the following sentences? a. B ∨ C. b. ¬A ∨ ¬B ∨ ¬C ∨ ¬D. c. (A ⇒ B) ∧ A ∧ ¬B ∧ C ∧ D