Southern New Hampshire University MAT 299 Module One Homework SNHU MAT299 Page 1 of 4 Module One Homework
Southern New Hampshire University 1. Analyze the logical forms of the following statements. Use A to represent "Alice has a dog," B to represent "Bob has a dog," and C to represent "Carol has a cat" to write each as a symbolic statement. a. Either Alice or Bob has a dog. AvB b. Neither Alice nor Bob has a dog, but Carol has a cat. (-Av-B) AC c. Either Alice has a dog and Carol has a cat, or Bob has a dog and Carol does not have a cat. (AAC) V (BA-C) This is similar to examples and exercises in Section 1.1 of your SNHU MAT299 textbook. 2. If D stands for "Doug is tall" and E stands for "Edie is short," what English sentences are represented by the following expressions? a. (DA E) v -D Doug is tall and Edie is short or Doug is not tall b. (D v -E) A -(D A E) Either Doug or Edie is tall and Doug is short or Edie is tall (I applied De Morgan's law) C. - DA [ (EAD) v -E ] Doug is short and either Edie is short and Doug is tall or Edie is tall This is similar to examples and exercises in Section 1.1 of your SNHU MAT299 textbook. 3. Make a truth table for the following formula. (G V -H) A - (G A L) This is similar to examples and exercises in Section 1.2 of your SNHU MAT299 textbook. G H L -H Gv-H T T T T T T F T F F T F T F F F F F F F T T F T T F F F T T F T T T T T F F T T GAL T F T F F F F F -(GAL) F T F T T T T T (Gv-H) A -(GAL) F T F T F F T T 4. Use truth tables to determine which of the following formulas are equivalent to each other. a. (J A K) V (-JA -K) b. J v K C. JA -K SNHU MAT299 Page 2 of 4 Module One Homework
Southern New Hampshire University d. - (-J v K) e. (J A -K) v K This is similar to examples and exercises in Section 1.2 of your SNHU MAT299 textbook. J K ¬ K JAK -JA-K (JAK) V (-JA -K) JvK JA-K -(-JvK) (JA-K) vK T T F T F F T F T T F F T T F T F F F F F T F F F F T T T F T T T F F F F T T T F T F F B and E C and D 5. Use truth tables to determine which of the following formulas are tautologies, which are contradictions, and which are neither. a. (M A -N) V (-M A