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Math 30-2 Set Theory & Probability: Lesson #2 Relationships Between Two Sets Objective: By the end of this lesson, you should be able to: - determine the intersection and the union of two sets, and use set notation to represent them. - solve problems involving two sets. Vocabulary Intersection of sets – Shade the part of each Venn diagram that represents the intersection of the two sets A and B. Intersecting Sets A Disjoint Sets Subsets A A B B B The intersection of sets A and B is denoted ______________. Union of sets – Shade the part of each Venn diagram that represents the union of the two sets A and B. Intersecting Sets A A A B Disjoint Sets Subsets B The union of sets A and B is denoted ________________. B Math 30-2 Set Theory & Probability: Lesson #2 e.g. 1) Put the numbers from 1 to 10 in the Venn diagram below. P is the set of prime numbers between 1 and 10, and O is the set of odd numbers between 1 and 10. (U is the universal set.) U (all numbers between 1 and 10) P O a) Describe in words what is meant by P O . List the elements in this set. b) Determine nP O. c) Describe in words what is meant by P O . Then determine nP O. d) You can also find the complement of the intersection or the union of two sets. In the context of the situation, describe what is meant by each, and list the elements in each set i) P O ii) P O Math 30-2 Set Theory & Probability: Lesson #2 e) Are the sets P and O disjoint? Explain. f) Is the set P O a subset of O? Explain. g) Is the set P O a subset of O? Explain. e.g. 2) Jacquie says that finding the union of sets is like adding two numbers, so n A B n A nB . Explain what is wrong with her formula and write a correct formula. Are there any cases when her formula would work? Principle of Inclusion & Exclusion For any two sets A and B: e.g. 3) Consider a standard deck of 52 cards: Four suits: clubs (C), spades (S), hearts (H), diamonds (D) - clubs & spades are black (B); hearts & diamonds are red (R) Each suit has 13 cards: ace to 10, and 3 face cards: Jack (J), Queen (Q), King (K) (See p. 24 for a visual representation of the cards in a standard deck.) a) Name a pair of disjoint sets from the sets listed above. Find the number of elements in the union and intersection of the two sets you chose. Math 30-2 Set Theory & Probability: Lesson #2 b) Describe what R K means, and list the elements in that set. c) In the game Hearts, the card(s) in the set H is/are each worth one point, and the card(s) in the set Q S is/are worth 13 points. Describe these two sets in words. d) Determine nS J . e) Describe the cards in the set S J . Then find nS J . e.g. 4) The set U has subsets A and B. n A 17 , nB 30 , and n A B 8 . a) Are A and B disjoint sets? Explain how you know. b) Find n A B . Assignment: p. 20-21 #1-2 p. 32-35 #1-5, 17