1.1 Set Notation
Sets are written like this: A = {1,2,3,4,5} Symbols: = is an element of = is not an element of # = Cardinal number (number of elements) #Q = the number of elements in the set Q Describing a set: List Method: The Rule Method - List the elements in the brackets - Describe using words {2,3,4,5,6} {even numbers between 1 and 11} Equal Sets: Two sets are equal if they have the same elements. E.g : Q = {2,3,9,11} P = {9,3,11,2} Q = P The Null Set: A set that has no elements is a null set or an empty set. Symbol: ( ) 1.2 Subsets | Facts to remember A divisor of a number is any whole number that divides evenly into that number. E.g : 3 divides evenly into 9. 3 is a divisor of 9. A prime number is a number that has two divisors only - 1 and itself. E.g : 13 is a prime number because only 13 and 1 divide into it. Remember! An element may only appear once in a set |
When elements are present in set A and set B, A is said to be a subset of B. Symbol: If all the elements in the subset A are the same in set B, then A is an improper set. If A is a subset of B, but does not contain all the same elements as B, then A is a proper set. 1.3 Venn Diagrams, Union and Intersection | If a set has n elements, then it will have 2n subsets |
Venn Diagrams are a way of representing sets in diagram form. Union and Intersection : The union of two sets is the set of elements contained in both sets. The union of two sets is written as : A U B The intersection of two sets is the set of elements that are common to both sets. The intersection of the two sets A and B is written as : A B Commutative Properties of Sets A U B = B U A, for every set A and B. We say that union is a commutative operation. A B - B A, for every set A and B. We say that intersection is a commutative operation |
1.4 The Universal Set
The universal set is the set that contains all elements. The letter U is used to show the universal set. Complement of a Set : The complement of a set A is the set of elements in the universal set U that are not elements of A. The complement of a set A is denoted by A' Set Difference : X/Y is the set of elements that are in X but not in Y | Every set is a subset of the universal set. |