CMSC150 Introduction to Discrete Math Summer 2015 Homework 5 July 11, 2015 The total number of points is 10. Your total score will be divided by 10 to produce a score over 100. Show all work. 1 Which of the following are statements? 4 points (1 point each) 1. She is a mathematics major. 2. 128=26 3. All that glitters is not gold. 4. Sleep tight and don't let the bedbugs bite. 2 Let A, B, and C be the following statements: A: John is healthy B: John is wealthy C: John is wise Use A, B, and C as dened above to translate the following statements into symbolic form.3 points (1 point each) 1. John is not wealthy but he is healthy and wise. 1 2. John is neither healthy, wealthy, nor wise. 3. John is wealthy, but he is not both healthy and wise. 3 Simplify the following proposition to 2 logic operations using the laws of the algebra of propositions. Write each step on a separate line with the algebra law you used as a justication. Missing steps will be penalized. (1 point) (P Q ) (P Q) (P Q ) 4 Justify each step with a comment in the proof sequence below for [A (B C)] B C A (1 point) 1. A (B C) 2. B' 3. C' 4. B C 5. (B C) 6. A' 5 Prove using a proof sequence that the argument is valid (hint: the last A' has to be inferred). Justify each step with a comment. (1 point) (A C) (C B ) B A 2