Question 1 A cafeteria offers a multiple-choice-set-lunch (MCSL). Offered at a standard price, in addition to the soup-of-the-day and bread-and-butter, each MCSL allows the customer to choose freely at most one item from the daily available choices in each of the four courses namely salad, main course, dessert, and beverage. Today, the available choices of salads are green-salad or fruit-salad; the available choices of main course are steak or pork-chop or fish-fillet; the available choices of dessert are apple- pie or cheese-cake or egg-pudding or ice-cream; the available choices of beverage are coffee or tea or cream-soda or ice-tea. At Table-9, there are three students namely Albert, Bobo, and Calvin. Each of the three students at Table-9 has ordered a MCSL. Their individual choices are listed below. Albert : green-salad, steak, apple-pie, ice-tea Bobo : fruit-salad, fish-fillet, apple-pie, tea Calvin : steak, apple-pie, cream-soda By using layman English, rewrite and determine the truth value of each of the following statements: (a) 3 an item P such that students x at Table - 9,x chooses P. (b) 3 a student x at Table - 9 such that Vitems P,x chooses P. (e) 3 a student x at Table - 9 such that courses C, 3 an item Pin C such that x chooses P. (d) students x at Table - 9,3 a dessert P such that x chooses P. (e) students x at Table - 9 and courses C, 3 an item Pin C such that x chooses P. Question 2 Given that the reciprocal of a real number x is a real number y such xy=1. Rewrite each of the following propositions by using symbolic quantifiers and variables. (a) Every nonzero real number has a reciprocal. (b) There is a real number with no reciprocal. Question 3 Rewrite each of the following statements by using symbolic quantifiers and variables. (a) There is a smallest positive integer. (b) There is no smallest positive real number. Question 4 By using layman English, rewrite each of the following statements, and then write a negation for the statement: (a) colours A, 3 an animal B such that Bis coloured A. (b) 3 a book A such that people B, B has read A. (c) Vodd integers A, 3 an integer B such that A = 2B +1. (d) va R, 3 a real number b such that a + b = 0. Question 5 Rewrite the statement: "Everybody is older than somebody." in the form vx, Question 6 Rewrite the statement: "Somebody is older than everybody." in the form 3 _x such that Question 7 By using symbolic quantifiers and variables, rewrite the statement: "Everybody loves somebody." Then write a negation for it. Question 8 By using symbolic quantifiers and variables, rewrite the statement: "Somebody loves everybody." Then write a negation for it. Question 9 By using symbolic quantifiers and variables, rewrite the statement: "There is a computer program which gives a correct answer to every question that is posed to it." Then write a negation for it. Question 10 By using symbolic quantifiers and variables, rewrite the statement: *Any even integer equals twice of some integer." Then write a negation for it
