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SETS & SET NOTATION Set • It is a collection of objects that have something in common or follow a rule. • The objects in the set are called its elements. • Set notation uses curly braces, with elements separated by commas. A = {coat, hat, scarf, gloves, boots}, • Set A has 5 elements. • Coat A What is the set of all fingers? What is the set of even numbers between 0 and 10? Let M = set of the days of the week. Let X = the set of odd numbers less than 12 B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} C = {2, 4, 6, 8, 10} • Subset – is part of a set. • Set C is a subset of set B. • We call set B the universal set…Venn Diagram is: U = {a, b, c, d, e, f, g, h, i, j, k, l, m} A = {a, c, e, g, i, k, m} B = {b, d, f, h} U = {a, b, c, d, e, f, g, h, i, j, k, l, m} A = {a, c, e, g, i, k, m} B = {a, b, c, d, e, f} U = {a, b, c, d, e, f, g, h, i, j, k, l, m} A = {a, b, d, e, h, j, m} B = {a, d, e, f, g, h, k} C = {b, c, f, h, l} Union • It is the joining of all elements of two or more sets • It is represented as A B. A = {letters in the word mathematics} B = {letters in the word problem} • Find A B A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} B = {set of odd numbers} C = {multiples of three} D = {Multiples of four} Find: B C= CD= B D= BCD= Intersection • This consists of the elements that the sets have in common. • It is represented as A B. A = {letters in the word mathematics} B = {letters in the word problem} • Find A B A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} B = {set of odd numbers} C = {multiples of three} D = {Multiples of four} Find: B C= CD= B D= BCD= Shade A B Shade A B Shade A B C Complement • Consists of the elements not in that set. • Represented as A’ • Read “not A” U = {1, 2, 3, 4, 5, 6, 7,8, 9, 10} A = { 2, 4, 6, 8, 10} B = {1, 2, 3, 4, 5, 6, 7} There are 18 bikes in a parking lot. 7 are gas powered and 5 are electric powered. 2 bikes are powered by both gas and electric. How many bikes in the parking lot are not powered by anything? A case of chocolate contains 15 chocolate bars. The chocolates come in three varieties: milk, dark, and milk/dark mix. 6 milk chocolates and 3 dark chocolates become expired. How many of the milk chocolates are expired if there are 6 milk chocolates that are not expired? • http://www.univie.ac.at/moe/tests/mengen/duv.html Homework • Worksheet