College Algebra & Trigonometry Asian College of Aeronautics AVT 1

SETS Set is any well-defined list, collection, or class of objects. Ex. 1. The set of counting numbers less than The set of letters in the English alphabet. 3. The set of letters in the word “Philippines”.

Set Notation A, B, C, D, X, YNames of Set or Set identifiers { }Enclosed an element(s) of a set ∈ An element of ∉ Not an element of ⊂ A subset of ⊊ Not a subset of A(N)Cardinal number of a set A={ ∅ } Null or empty set

Set Descriptions Roster Method Tabulation / List Rule Method Descriptive / Definitive A = {1,2,3,4,5,6,}A = {x/x is a counting number less than 6} The set if counting numbers less than 6.

Set Definitions Finite SetConsists of a specific number of different elements. A = {1,2,3,4,5,6} Infinite SetIt has unlimited number of elements. A = {x/x is an even number} A = {2, 4, 6, 8,...} Empty or Null SetIt has no element A = { } or A = { ∅ } Equal SetsSets having the same elements regardless of the order of occurrence. A = {r, a, t} B = {a, r, t} ∴ A = B Equivalent SetsSets having the same number of elements such that they have one-to-one correspondence. A = {a, b, c} B = {1, 2, 3} ∴ A ≈ B Universal SetSet consisting of the totality of elements under consideration.

OPERATIONS ON SETS UNION OF TWO SETSSets A & B is defined to be composed of all elements which belong to A or to B or to both A & B. SYMBOL: ⋃ Example: A = { 1,2,3} B = {3,4,5} A ⋃ B = {1,2,3,4,5} INTERSECTION OF TWO SETS Set of all elements that belong to both A and B. SYMBOL: ⋂ Example: A = {1,2,3} B = {3, 4,5} A ⋂ B = {3}

OPERATIONS ON SETS SET COMPLEMENTSet A as a given set; the complement of A refers to all elements of the universal set that does not belong to the given set A. SYMBOL: prime (‘) Example: U = {1,2,3,4,5,6,7,8,9} A = {1,2,3,4,5,6,7,8} A’ = {9} CARTESIAN PRODUCTSet of all ordered pairs. SYMBOL: × Example: A = {1,2} B = {a,b A × B = {(1,a),(1,b),(2,a),(2,b)}