Sets and Venn Diagrams Prime Numbers Odd Numbers
Sets and Venn Diagrams {} Prime Numbers Odd Numbers Even Numbers
Sets A B C {} A SET is a collection of objects. They can be numbers, words or things. SETS are named using a capital letter. Objects are listed inside brackets. A = {2, 3, 5, 7, 11, 13} B = {square, rectangle, trapezoid, rhombus, parallelogram} C = {desk, chair, students, whiteboard, computer, teacher} Make Awesome Things Happen
Element (of a Set) An ELEMENT of a set is a member of the set. The symbol “ ” means “is a member of” and the symbol “ ” means “is not a member of” 7 A A = {2, 3, 5, 7, 11, 13} 10 A Make Awesome Things Happen
Subset (of a Set) A SUBSET of a set is a set that contains some or all of the elements of the set, but no other elements. The symbol “ ” means “is a subset of” and the symbol “ ” means “is not a subset of”. A = {2, 3, 5, 7, 11, 13} B = {3, 5, 7} C = {1, 2, 3, 4} B A C A Make Awesome Things Happen
Subset (of a Set) A B B A Make Awesome Things Happen
Union (of 2 Sets) A UNION of 2 sets is a set that contains all of the elements of both sets. Common elements are listed only once. The symbol “ ” means “union of”. A = {3, 5, 7, 9} B = {1, 2, 3, 4, 5, 6} A B= {1, 2, 3, 4, 5, 6, 7, 9} Make Awesome Things Happen
Union (of 2 Sets) B A x, 1, 2, 4 3 w, y, z A = {1, 2, 3, 4, x} B = {3, w, x, y, z} A B = {1, 2, 3, 4, w, x, y, z} Make Awesome Things Happen
Intersection (of 2 Sets) An INTERSECTION of 2 sets is a set that contains only those elements that are in both sets. The symbol “ ” means “intersection of”. A = {3, 5, 7, 9} B = {1, 2, 3, 4, 5, 6} A B = {3, 5} Make Awesome Things Happen
Intersection (of 2 Sets) B A x, 1, 2, 4 3 w, y, z A = {1, 2, 3, 4, x} B = {3, w, x, y, z} A B = {x, 3} Make Awesome Things Happen
{} Empty or Null Set An EMPTY OR NULL SET is a set that contains no elements. The symbols “{} or ” stand for an empty or null set. A = {3, 5, 7, 9} B = {2, 4, 6, 8} A B = {} or A B= Make Awesome Things Happen
{} Empty or Null Set B A 1, 2, 3, 4 x, w, y, z A = {1, 2, 3, 4} B = {w, x, y, z} A B = {} or Make Awesome Things Happen
A’ Complement The COMPLEMENT of set A is all elements of the universal set, U, not in set A. The Universal set will be defined for the situation. The complement is denoted with a ’. U = Odd numbers < 10 A = {1, 5, 9} A’ = {3, 7} Make Awesome Things Happen
A’ Complement U = Factors of 24 A 1, 2, 3, 4, 6 A = {1, 2, 3, 4, 6} A’ = {8, 12, 24} Make Awesome Things Happen
Additional Terms Types of Set Notation: • Description Notation (describes the set) I = the set of integers A = the set of odd numbers less than 20 • Roster Notation (lists the elements of the set) I = {…, -3, -2, -1, 0, 1, 2, 3, …} A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} • Set Builder Notation (gives the property that defines each element) I = {x|x is an integer} A = {x|x is an odd whole number less than 20} Make Awesome Things Happen
Additional Terms • Infinite Set: a set whose elements cannot be counted or listed I = {…, -3, -2, -1, 0, 1, 2, 3, …} • Finite Set: all elements can be counted or listed A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} Make Awesome Things Happen
Additional Terms • Equal Sets: two sets that contain the same elements but not necessarily in the same order A = {c, 0, 1, d} B = {d, 1, 0, c} • Equivalent Sets: two sets that contain the same number of elements A = {1, 2, 3} B = {4, 5, 6} Make Awesome Things Happen
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