Consider the following predicates: M(x): x is a movie A(x): x is an actor P(x): x...

 

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Consider the following predicates: M(x): x is a movie A(x): x is an actor P(x): x is popular S(x, y): x stars in y Task 4A. (10 marks, 2 marks per formula) Using the predicates given above, translate each of the following sentences into a formula of predicate logic: 2. Only actors star in movies, and only movies are starred in by actors. 3. Some movies are popular, and some movies are not popular. 4. At least one popular actor stars in every popular movie. 5. At least one actor who is not popular stars in every movie. Task 4B. (10 marks) Let I be an interpretation with domain D satisfying your formulas for (1)-(5). Argue that, given any m E D such that I(M)(m) and I(P) (m) are both true, we have two distinct a1, a2 E D such that I(S)(a, m) and I(S)(a, m) are both true. Consider the following predicates: M(x): x is a movie A(x): x is an actor P(x): x is popular S(x, y): x stars in y Task 4A. (10 marks, 2 marks per formula) Using the predicates given above, translate each of the following sentences into a formula of predicate logic: 2. Only actors star in movies, and only movies are starred in by actors. 3. Some movies are popular, and some movies are not popular. 4. At least one popular actor stars in every popular movie. 5. At least one actor who is not popular stars in every movie. Task 4B. (10 marks) Let I be an interpretation with domain D satisfying your formulas for (1)-(5). Argue that, given any m E D such that I(M)(m) and I(P) (m) are both true, we have two distinct a1, a2 E D such that I(S)(a, m) and I(S)(a, m) are both true.