# Question: Consider a vocabulary with only four propositions A B C

Consider a vocabulary with only four propositions, A, B, C, and D. How many models are there for the following sentences?

a. (A Λ AB) V (B Λ C)

b. A V B

c. A ↔ B ↔ C

a. (A Λ AB) V (B Λ C)

b. A V B

c. A ↔ B ↔ C

**View Solution:**## Answer to relevant Questions

We have defined four different binary logical connectives.a. Are there any others that might be useful?b. How many binary connectives can there be?c. Why are some of them not very useful?Minesweeper, the well-known computer game, is closely related to the wumpus world. A minesweeper world is a rectangular grid of N squares with M invisible mines scattered among them. Any square may be probed by the agent; ...Consider a knowledge base containing just two sentences: P(α) and P(h). Does this knowledge base entail V x P(x)? Explain your answer in terms of models.Rewrite the propositional wumpus world facts from Section 7.5 into first-order logic. How much more compact is this version?Prove from first principles that Universal Instantiation is sound and that Existential Instantiation produces an inferentially equivalent knowledge base.Post your question