Artificial Intelligence (2014-2015) Tutorial Propositional Logic Question A proposition or statement is a sentence which is either true or false In the following sentences, which one is proposition? C om The sun is shining The sum of two prime numbers is even 3+4=7 It rained in Austin, TX, on October 30, 1999 x+y > 10 Is it raining? Come to class! n is a prime number ne a b c d e f g h Question en Vi Question P ∧ ¬P P ∨ ¬P (P ⇒ Q)⇒(P ⇒ Q) (P ∨ Q)⇒(P ∧ Q) nh a b c d Zo For each of the following propositions, construct a truth table and state whether the proposition is valid or satisfiable (you can just write one truth table with many columns) Si Show that the following formulas are tautologies: a ¬(A ∧ B) ⇔ ¬A∨¬B b A⇒B ⇔ ¬B ⇒¬A c ((A⇒B) ∧ (B ⇒A)) ⇔ (A ⇔ B) d (A ∨ B) ∧ (¬B ∨ C)⇒(A ∨ C) Question Solve the following case: “If the criminal had an accomplice, then he came in a car The criminal had no accomplice and did not have the key, or he had the key and an accomplice The criminal had the key Did the criminal come in a car or not?” SinhVienZone.com https://fb.com/sinhvienzonevn Question Si nh Vi en Zo ne C om Formalise the following and, by writing truth tables for the premises and conclusion, determine whether the arguments are valid a Either John isn’t stupid and he is lazy, or he’s stupid John is stupid Therefore, John isn’t lazy b The butler and the cook are not both innocent Either the butler is lying or the cook is innocent Therefore, the butler is either lying or guilty SinhVienZone.com https://fb.com/sinhvienzonevn