Question

Help me solve this 7 Mathematical logic questions

Mathematical Logic Homework1 1)Write out the truth tables for the following. a) (A B) V(A) 2) Determine whether the following are tautologies. DO NOT USE A TRUTH TABLE. b) (AAB) (AVC) c) (A B)]-A 3) Write out the following as statement forms using statement letters to stand 10 atomic sentences -that is, those sentences that are not built out of other sentences. a) If Mr. Jones is happy, Mrs Jones is not happy and if Mr. Jones is not happy Mrs Jones is not happy. b) Either Sam will come to the party and Max will not, or Sam will not come to the party and Max will enjoy himself. c) A sufficient condition for x to be odd is that x is prime. d) A necessary condition for a sequence s to converg is that s be bounded. e) A necessary and sufficient condition for the sheikh to be happy is that he was wine, women and song. Fiorello goes to the movies only if a comedy is playing g) The bribe will be paid if and only if the goods are delivered. h) If x is positive, x2 is positive. Karpov will win the chess to i) 4)Determine whether the following pairs are logically equivalent. You can use any method. Give a counterexample if a pair is not logically equivalent. a) (IA -B-A) and A b) A B and (A B) A (B A) c) -AvB and -BVA e) AV(B艹c) and (A VB)-→ (AVC) 5) Prove: A-+ B is logically equivalent to (A ^ B). 6) which of the following is logically implied by A ^ B? a) A b)B c) A VB d) nA VB e)-B →A A B g)A B 7) If A → B is T, what can be deduced about the truth values of the following? a) (AVC)-(BVC) b) (AAC)-(BAC) 8) Show the logical equivalence of-CA艹B) and (A ^-B) V (-A ^ B). 9) Find the statement forms in the connectives "and", "or" and "not" that have the following truth functions

Answer 1

リ true Tnw

e and う (BAC A C AA C