1. Prove that the propositional logic sentence A+BA(-A V B) is valid, inconsistent or satisfiable. Discuss your answer briefly. 2. Convert the following English sentences to first-order predicate calculus. a) Everyone likes cakes. b) Johan is Mariam's brother. c) The day is Saturday. d) Some students took IAS2313 in semester 11834. e) There is only fruit on the table. f) Everyone taking Al is smart. Nobody likes mouse h) Everyone likes cakes. i) Person x is born in country c. j) All freighters are ships. State the conclusion and rule of inference used for each of the followings: 3. a) If today is Tuesday, then I go to class Today I don't go to class. b) If today is Tuesday, then I go shopping If I go shopping, then I buy shoes 4. Show that S is valid inference from the following premises: P-Q QVR -SP R