Sets And Set Operations Pdf

Let a and b be arbitrary sets.

Sets and set operations pdf. In section 2 1 we used logical operators conjunction disjunction negation to form new statements from existing statements in a similar manner there are several ways to create new sets from sets that have already been defined. Set theory set theory operations on sets. Two sets are equal if and only if they have the same elements. Set operations two sets can be combined in many different ways.

2 union let a and b be sets. Georg cantor one of the founders of set theory gave the following definition of a set at the beginning of his beiträge zur begründung der transfiniten mengenlehre. For example suppose that committee a consisting of the 5 members jones blanshard nelson smith and hixon. The union of a and b written a b is the set whose elements are just the elements of a or b or of both.

Numbers people letters of the alphabet other sets and so on. We define several operations on sets. 1 2 3 3 1 2 1 2 1 3 2 note. The union of a and b denoted by a b is the set containing those elements that are either in a or in b or in both.

Let k a b l c d and m. E relations and functions are the ways to connect and work with the sets. Set operations can be used to combine sets. A set is a well defined collection of distinct objects.

Duplicates don t contribute anythi ng new to a set so remove them. Given below is the source code for some of the basic set operations. Here are some useful rules and definitions for working with sets. Sets help in distinguishing the groups of certain kind of objects.

The symbol is employed to denote the union of two sets. Whereas set operations i. See this for set theory introduction. By default the program works only on integers but can be modified in the main function to run for other data types also.

Thus the set a b read a union b or the union of a and b is defined as the set that consists of all elements belonging to either set a or set b or both. In the predicate notation the definition is a b def x x a or x b examples. The objects that make up a set also known as the set s elements or members can be anything. 4 cs 441 discrete mathematics for cs m.

Sets relations and functions are the tools that help to perform logical and mathematical operations on mathematical and other real world entities. The order of the elements in a set doesn t contribute.