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LET’S TALK ABOUT SETS (Sets and Venn Diagrams) SET: UNIVERSAL SET (S): SUBSET (): a group of items called elements or members ex. A = {1, 2, 3, 4, 5} 3 A “3 is an element of set A” the set containing ALL elements being considered a set whose elements are also elements of another set ex. if all elements of set C are also elements of set A then C A every set is a subset of itself EMPTY (NULL) SET: a set that contains NO elements denoted using { } or VENN DIAGRAM: depicts relationships among sets named after the logician, John Venn (1834-1923) S S A Subset: A S Universal Set S S A B Intersection: A B “and” set A and B contain COMMON elements A B Union: A B “or” elements belong to set A or set B Example List all subsets of the set A = {1, 3, 5}. Example Given the sets, A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, list the elements of each of the following: a) S = b) A B = c) A B = d) A S = Example List the elements in each of the following sets: a) {x 3 < x ≤ 8, x N } = b) { factors of 12 } = SETS: The Basic Concepts (Worksheet) 1. List the members of each of the following sets: a) b) c) d) e) the set of vowels in the English language the set of positive odd integers less than 10 the set of months beginning with the letter J { x 1 x 7, x N } the set of real numbers x, for which x2 = –1 2. Give all the subsets of {3,6}. 3. Which of the following statements are true? a) b) c) d) e) f) 4. Let A = {3, 8, 12, 16, 19}, B = {0, 1, 3, 4, 7}, C = {8, 12, 19}, and D = {8, 12}. a) b) 5. List all pairs of sets in which one is a subset of the other. List all pairs of sets such that one is not a subset of the other. List the elements in each of the following sets: a) b) c) 6. 3 {2, 3, 4, 5} 5 {1, 3, 5, 7, 9} {1, 2, 3} = {3, 1, 2} the set of all natural numbers less than 5 is {1, 2, 3, 4} { x x 6, x N } = {1, 2, 3, 4, 5} 7 is a member of the set of odd whole numbers { one-digit even whole numbers } { factors of 24 } { prime numbers between 10 and 50 } Write a description of each of the followings sets: a) {1, 5, 10, 25, 100, 200} b) {2, 3, 5, 7, 11, 13} ANSWERSANSWERSANSWERS 1.a) d) 2.a) 3.a) e) 4.a) 5.a) 6.a) b) {a,e,i,o,u} b) {1,3,5,7,9} c) {January, June, July} {2,3,4,5,6,7} e) { } { }, {3}, {6}, {3,6} true b) false c) true d) true false f) true C A, D A, D C b) (A,B), (B,C), (B,D) {2,4,6,8} b) {1,2,3,4,6,8,12,24} c) {11,13,17,19,23,29,31,37,41,43,47} the set of Canadian coin values the set of natural prime numbers less than or equal to 13