SET RELATIONS

Set OperationsLecture 3February 10, 2015UNIONThe union of two sets A and B is the set consisting of all elements belonging to either sets A or set B.

SET PERATIONS

2UNIONExample:A = {1, 2, 3, 5, 7, 11}B = {1, 3, 5, 7, 9}

Then A U B =SET PERATIONS3 A B

SET PERATIONS4Examples

.SET PERATIONS

Examples

.

SET PERATIONS

INTERSECTIONThe intersection of two sets A and B is the set of all elements common to both set A and set B.

SET PERATIONS7INTERSECTIONExample:If A = {2, 4, 6, 8, } and B = {5, 10, 15, }

Then A B = { __________________ }.Describe A B using the rule method.SET PERATIONS8INTERSECTIONIf A B = , we say A and B are disjoint.

Example: Let V be the set of all vowels in the English alphabet and let C be the set of all consonants. What is V C?Hence, sets V and C are _____________.SET PERATIONS9INTERSECTIONA B

SET PERATIONS10Examples

SET PERATIONSQUIZ no. 3

COMPLEMENTThe complement of a set A is a set whose elements are in the Universal set but not in A.

SET PERATIONS13COMPLEMENTExample:If U is the set of all letters in the English alphabet and A be the set of all vowels in the English alphabet. Then

SET PERATIONS14COMPLEMENT

Set OperationsA15Examples

SET PERATIONSDIFFERENCEDescribe in words the difference of two sets.

SET PERATIONS17DIFFERENCEExample:Let A = {1, 3, 5, 7, 9} and B = {3, 5, 13}

Then A B = { ________________ }.What is B A?SET PERATIONS18DIFFERENCE

UA BABSET PERATIONS19Examples

SET PERATIONSCROSS PRODUCTThe elements of A x B are called ordered pairs.

SET PERATIONS21CROSS PRODUCTExample:Let A = {1, 2, 3} and B = {a, b}.

Then A x B = { (1,a), (1,b), (2,a), (2,b), (3,a), (3,b) }.How many elements does A x B have?What is B x A?SET PERATIONS22CROSS PRODUCT

A123BabSET PERATIONS23