Sets And Set Operations Pdf

The symbol is employed to denote the union of two sets.

Sets and set operations pdf. We define several operations on sets. Duplicates don t contribute anythi ng new to a set so remove them. 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. Two sets are equal if and only if they have the same elements.

Given below is the source code for some of the basic set operations. 2 union let a and b be sets. 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 operations can be used to combine sets.

By default the program works only on integers but can be modified in the main function to run for other data types also. Let k a b l c d and m. 1 2 3 3 1 2 1 2 1 3 2 note. Sets help in distinguishing the groups of certain kind of objects.

Numbers people letters of the alphabet other sets and so on. 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. The order of the elements in a set doesn t contribute. E relations and functions are the ways to connect and work with the sets.

An introduction to sets set operations and venn diagrams basic ways of describing sets use of set notation finite sets infinite sets empty sets subsets universal sets complement of a set basic set operations including intersection and union of sets and applications of sets with video lessons examples and step by step solutions. Set operations two sets can be combined in many different ways. See this for set theory introduction. A b x x a x b u b a.

Set a b c contains an element which is present in all the sets a b and c i e 0. 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. Sets relations and functions are the tools that help to perform logical and mathematical operations on mathematical and other real world entities. 4 cs 441 discrete mathematics for cs m.

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. The objects that make up a set also known as the set s elements or members can be anything. For example suppose that committee a consisting of the 5 members jones blanshard nelson smith and hixon. A set is a well defined collection of distinct objects.

Set theory set theory operations on sets. In the predicate notation the definition is a b def x x a or x b examples.