Set Theory And Notation
Overview
Every time you filter search results, group customers by two overlapping criteria, or ask how many students take both Physics and French, you are reasoning about sets. Set notation gives that reasoning a precise, compact language instead of long sentences.
You will use curly-brace notation and membership symbols, work with union, intersection and complement (including sets defined algebraically), count elements with the \(n(A)\) notation, and solve two- and three-set Venn diagram problems, including ones where a region is left as an unknown to find by equation.
Objectives
- Understand the idea of a set
- Use set language and notation
- Understand and use union and intersection of sets, including sets defined in algebraic terms
- Find the number of elements in a set using the notation n(A)
- Understand and use complementary sets with the notation A'
- Understand and use subsets
- Understand and use the universal set and null set
- Use Venn diagrams and their application in simple logical problems
- Use symbols to represent sets
Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Set Theory And Notation. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Which symbol means 'is not an element of'? A) The union symbol B) The subset symbol C) The not-an-element-of symbol D) The complement symbol Answer: C
- If A = {2, 3, 5, 7} and B = {1, 3, 5, 9}, what is A intersection B? A) {1, 2, 3, 5, 7, 9} B) {3, 5} C) {2, 7} D) {1, 9} Answer: B
- The universal set is {1, 2, 3, 4, 5, 6, 7, 8} and C = {2, 4, 6, 8}. What is C complement? A) {1, 3, 5, 7} B) {2, 4, 6, 8} C) The empty set D) {1, 2, 3, 4} Answer: A
- If n(P) = 20, n(Q) = 14 and n(P intersection Q) = 6, what is n(P union Q)? A) 6 B) 28 C) 34 D) 40 Answer: B
- Which statement about the empty set is always true? A) It is a subset of every set B) It contains one element C) It equals the universal set D) It cannot be a subset of any set Answer: A
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