a) Write each of these statements in the form if p, then q in English. [Hint:...

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a) Write each of these statements in the form "if p, then q" in English. [Hint: Refer to the list of common ways to express conditional statements.] i. It is necessary to wash the boss's car to get promoted. ii. Winds from the south imply a spring thaw. i1. [1 mark] [1 mark] A sufficient condition for the warranty to be good is that you bought the computer less than a year ago. Willy gets caught whenever he cheats. [1 mark] [1 mark] iv. b) Let p be "Bonsu is rich" and let q be "Bonsu is happy". Write each of the following in symbolic form using logical operators or connectives. i. Bonsu is poor but happy; Bonsu is neither rich nor happy; Bonsu is either rich or unhappy; and Bonsu is poor or else he is both rich and unhappy. [1 mark] [1 mark] [1 mark] [2 marks] 11. 111. iv. c) Let P(x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer engineering courses at your school. Express each of these quantifications in English. i. 3xayP(x, y) ii. 3xVyP(x, y) VxayP(x, y) 3YVXP(x, y) VyaxP(x, y) VxVyP(x, y) [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] 111. iv. V. vi. a) Write each of these statements in the form "if p, then q" in English. [Hint: Refer to the list of common ways to express conditional statements.] i. It is necessary to wash the boss's car to get promoted. ii. Winds from the south imply a spring thaw. i1. [1 mark] [1 mark] A sufficient condition for the warranty to be good is that you bought the computer less than a year ago. Willy gets caught whenever he cheats. [1 mark] [1 mark] iv. b) Let p be "Bonsu is rich" and let q be "Bonsu is happy". Write each of the following in symbolic form using logical operators or connectives. i. Bonsu is poor but happy; Bonsu is neither rich nor happy; Bonsu is either rich or unhappy; and Bonsu is poor or else he is both rich and unhappy. [1 mark] [1 mark] [1 mark] [2 marks] 11. 111. iv. c) Let P(x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer engineering courses at your school. Express each of these quantifications in English. i. 3xayP(x, y) ii. 3xVyP(x, y) VxayP(x, y) 3YVXP(x, y) VyaxP(x, y) VxVyP(x, y) [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] 111. iv. V. vi.