Calgary Board of Education CBe-Learn Page 1 of 2 Mathematics 20-2 Assignment #4: Inductive and Deductive Reasoning Cherpen [11] Show all calculations and reasoning in your answers. You must use methods taught in this course to receive full marks for your answers. 1. Guilia created the following table to show a pattern. Multiples of 9 18 27 36 45 54 Sum of the Digits 9 9 9 9 Which conjecture could Guilia make, based solely on this evidence? Choose the best answer. A. The sum of the digits of a multiple of 9 is equal to 9. B. The sum of the digits of a multiple of 9 is an odd integer. C. The sum of the digits of a multiple of 9 is divisible by 9. D. Guilia could make any of the above conjectures, based on this evidence. 2. Mick and Sue were discussing what conjecture could be made regarding the prime number pattern shown. They both agreed to the following conjecture: "The sum of two prime numbers is an even number." 3+5=8 5+7=12 7 +11 = 18 13 + 17 = 30 19 + 23 = 42 29 + 31 = 60 a) Provide a counterexample that shows their conjecture is false. [1] b) Revise their conjecture so it holds true for prime numbers. [1] 3. Abby made the following conjecture: The sum of a multiple of 7 and a multiple of 8 will be an odd number. Do you agree or disagree? Briefly justify your decision with a counterexample if possible. CBe-Learn