Question

Consider the following set of propositions:

F1: If Mr. Sydney has a dog, then Mrs. Benson has a cat.

F2: If Mr. Johnson has a dog, then he has a cat, too.

F3: If Mr. Sydney has a dog and John has a cat, then Mrs. Presley has a dog.

F4: If Mrs. Benson and Mr. Johnson share a pet of the same species, then Mr. Sydney has a cat.

F5: Mr. Sydney and Mr. Johnson have dogs.

4.1. Translate the above reasoning into propositional logic formulas. Note: Please use s, j, b, p for atomic propositions that are true if Sydney, Johnson, Benson, or Presley (respectively) have a dog, and write S, J, B, P for Boolean variables that are true if they have a cat.

4.2. Lest F = F1 ∧ F2 ∧ F3 ∧ F4 ∧ F5. Check F for satisfiability using the Horn’s formula satisfiability test. If you verify that F is satisfiable, then present a model for it. Justify.

Answer 1