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Exploring Set Theory: Warm-Up Exercises and Practical Problems

This session focuses on reinforcing understanding of set theory through engaging exercises. Participants will work in pairs or small groups to solve problems involving set differences, intersections, and unions using the SETL environment. Specific problems include determining the number of elements in nested sets, calculating set differences between given sets, and utilizing the SETL website for problem-solving. This interactive approach aims to solidify the foundational concepts of set theory while encouraging collaboration and practical application of learned skills.

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Exploring Set Theory: Warm-Up Exercises and Practical Problems

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  1. C241 PLTL Session – 10/12/2014 Even more on sets!

  2. Warm-Up Exercise • Grab a worksheet • Begin completing the worksheet in pairs or small groups

  3. Problem 1 How many elements are in a set within a set?

  4. Problem 2 What is the set difference between (3, 4, 6, 2, 1) and ((), (3, 4, 6, 2, 1), 3, 2, 1)?

  5. Problem 3 Visit the SETL website, http://setl.org/setl-server.html, and answer the following questions: (Give both the answer and the SETL code that generated you this answer.) Note that sets are denoted by braces {}, the intersection operator for sets is denoted by *, and the union operator for sets is denoted + in SETL. Using parentheses, (), to denote a set is a more conventional notation than using braces, {}. A = (11, 4, 13, 4, 25, 6, (), (1, 2)), B = (1, 4, 25, 6, (), 17, 8, 9), and C = (4, 7, 8, 9, 10, (11, 12, 13), 12) (i) What is the set difference between A and C? (ii) What is the set difference between C and D = ((11, 12, 13))?

  6. Problem 4 from last week’s PowerPoint Visit the SETL website, http://setl.org/setl-server.html, and answer the following questions: (Give both the answer and the SETL code that generated you this answer.) Note that sets are denoted by braces {}, the intersection operator for sets is denoted by *, and the union operator for sets is denoted + in SETL. Using parentheses, (), to denote a set is a more conventional notation than using braces, {}. A = (11, 4, 13, 4, 25, 6, (), (1, 2)), B = (1, 4, 25, 6, (), 17, 8, 9), and C = (4, 7, 8, 9, 10, (11, 12, 13), 12) (i) What is the set difference between A and B? (ii) What is the set difference between C and D = (11, 12, 13)?

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