Artificial Intelligence (TEST) - COMPUTER SCIENCE

1. Given the following propositions: p: Peter is driving his own car. a: Andrew is late. m: Max has caught the bus. (a) Write each of the following in symbols: (i) Andrew is late and Peter is driving his own car. (ii) Either Max has caught the bus or else Andrew is late. (iii) Either Peter is driving his own car and Andrew is late or else Max has not caught the bus. (iv) Peter is driving his own car and either Andrew is late or else Max has caught the bus. (v) Max has caught the bus but Andrew is not late. (b) Translate into simple English: (i) (a ∧ p) ∨ (∼ a ∧ m) (ii) p ∨ (∼ m ∧ ∼ a) (iii) m ∧ (∼ p ∨ ∼ a) (iv) p ∧ m ∧a (v) (∼ a ∧ p) ∨ m 2. Construct truth tables for the following propositions: (i) (p ∨ ∼q) ∧ ( ∼p ∨ q) (ii) (q ∧ ∼r) ∨ (∼p ∧ r) (iii) ((p ∧ ∼q) → r) ∧ (∼p → ∼r) (iv) ((r → (q → p)) ∧ ~p) → ~r 3. Let P denote a set of people, and M a set of movies, and suppose that the predicate S(x, y) means that person x has seen movie y. (a) Translate each of these sentences into symbols: (i) For each movie there is somebody who has not seen it. (ii) Nobody has seen any of the movies. (iii) There is some movie that at least one person has not seen. (iv) There is at least one movie that some person has seen. (v) There is some person who has seen all the movies