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Problem Set A - Exercises

Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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MAT102S - Introduction to Mathematical Proofs - UTM Problem Set A - Spring 2010 Here are the Exercises assigned: 1.2. Fill in the blanks. The equation x 2 + bx + c = 0 has exactly one solution when , and it has no solutions when . 1.5. ( - ) Consider the Celsius (C) and Fahrenheit (F) temperature scales. C 0 5 10 15 20 25 30 F 32 41 50 59 68 77 86 Express the sentence “The temperature was 10 C and increased by 20 C ” using the Fahrenheit scale. 1.6. ( - ) At a given moment, let f and c be the values of the temperature on the Fahrenheit and Celsius scales, respectively. These values are related by f = (9 / 5) c + 32. At what temperatures do the following events occur? a) The Fahrenheit and Celsius values of the temperature are equal. b) The Fahrenheit value is the negative of the Celsius value. c) The Fahrenheit value is twice as the Celsius value. 1.7. ( - ) The statement below is not always true for x, y R . Give an example where it is false, and add a hypothesis on y that makes it a true statement.
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