Equations Algebra

Math 1313 Section 5.1 The Universal set is the set of interest in a particular discussion. A Venn diagram is a visual representation of sets. They look like: Set Operations Let A and B be two sets. The set of all elements that that belong to either A or B or both is called the Union of A and B (denoted A ∪ B). In set builder notation A ∪ B = {x | x∈ A or x∈ B or both} Set Union in a Venn diagram looks like: Popper 1 is A 3 Math 1313 Section 5.1 Let A and B be two sets. The set of all elements in common with both sets A and B is called the Intersection of A and B (denoted A∩B). In set-builder notation A∩B ={x | x∈ A and x∈ B} Set Intersection in a Venn diagram looks like: If A ∩ B = Ø, then we say the intersection is the null intersection and that A and B are disjoint. Let U be a universal set and A ⊆ U. The set of all elements in U that are not in A is called the Complement of A. (denoted ) In set-builder notation Ac ={x | x∈ U , x∉ A } Set Complementation in a Venn diagram looks like: 4 Math 1313 Section 5.1 Set Operations Let U be a universal set and A and B be subset of U U =∅ ∅ =U A∪A =U A∩ A =∅ A ∪B = B ∪ A A∩B =B∩A A =A DeMorgan’s Laws ∩ = ∪ ∪ = ∩ Example 3: Let U={1,2,3,4,5,6,7,8,9,10} A={1,3,5,7,9} B={2,4,6,8,10} C={1,2,4,5,8} Find the given sets. a. ∪ b. ∩ c. ∩ 5 Math 1313 d. e. f. ∪ ∪ Section 5.1 ∪ ∩ ∩ ∪ Example 4: Let U denote the set of all employees at a certain Company. Let T={x∈U| x likes to read Time magazine}, E={x∈U| x likes to read ESPN magazine} and C={x∈U| x likes to read Car and Driver}. Part A. Describe the given set in words given statement in set notation. i. T ∪ C = the set of all employees at this company that ii. ∩ ∪ = the set of all employees at this company that 6 Math 1313 Section 5.1 Part B. Describe the given statement in set notation. i. The set of all employees at this company that like ESPN and do not like Car and Driver. ii. The set of all employees at this company that do not like Time, ESPN or Car Driver. Another good example is example 8 and 9 in your book. Read through that example. Example 5: Shade the portion of the Venn diagram that represents the given set. (Assume the given sets are not disjoint.) a. ∩ b. ∪ ∩ Popper 3: Given the following sets, find ∩ = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10", a. b. c. d. e. . = 3, 4, 5, 7, 9, 10" and = 2, 3, 5, 7" {2, 3, 4, 5, 7, 9, 10" {3, 5, 7} {1, 6, 8} {4, 9, 10} None of the above 7 Math 1313 ∩ c. & Section 5.1 ∩ Popper 4: Given the following Venn diagram, which regions make up a. b. c. d. d. ∩ III and IV only. I, II and IV only. I only. Ø ∩ 8 Math 1313 Section 5.1 Popper 5: Given the following Venn diagram, which regions make up a. b. c. d. e. ∪ III and IV only. I, II and IV only. I only. Ø ∪ ∪ & 9