Sets and set operations pdf

Ice cream cones there are two types of ice cream cones, chocolate and vanilla. The shaded region of the venn diagram below corresponds to. If 15 people buy vanilla cones, and 20 people buy chocolate cones, how many people bought both chocolate and vanilla ice cream cones. Describing a set there are two distinct ways of describing the members of a set. The union of a and b, denoted by a b, is the set that contains those elements that are either in a or in b, or in both. A universal set for a particular problem is a set which contains all the elements of all the. Sets in math, 7th grade pdf printable math 4 children plus. The universal set u is the set containing all elements for the problem we are discussing. B x x a and x b this is the intersection of a and b. Set operations in linq refer to query operations that produce a result set that is based on the presence or absence of equivalent elements within the same or separate collections or sets.

Previously, sets have been represented diagrammatically in venn diagrams which show different relationships. The following figures give the set operations and venn diagrams for complement, subset, intersect and union. Georg cantor in the previous chapters, we have often encountered sets, for example, prime numbers form a set, domains in predicate logic form sets as well. The universal set is the set of interest in a particular discussion. Write the set, p, of all integers less than 100 that are powers of 2.

Set builder notation sets can also be described by using what is known as set builder notation. The objects that make up a set also known as the set s elements or members can be anything. 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, examples with step by step solutions. Sets and functions university of california, davis. Before the 19th century it was uncommon to think of sets as completed objects in their own right. A venn diagram can be a useful way of depicting sets and set operations. Jul 05, 2018 union, intersection,cross product, difference and complement.

B of two sets a, b is the set of all elements that belong to both a and b. Georg cantor, one of the founders of set theory, gave the following definition of a set at the beginning of his beitrage zur. One use of venn diagrams is to illustrate the effects of set operations. Refer to the diagram to answer the questions below. These problems are to be solved in general, not by referring to specific sets whose elements are known. A set can be represented by listing its elements between braces. The union of a and b, denoted by ab, is the set containing those elements that are either in a or in b, or in both.

This involves stating some property or properties that all elements of the set must have. Set theory \a set is a many that allows itself to be thought of as a one. The objects in a set are called the elements of the set. We can, of course, include more than two sets in a venn diagram. You and 24 of your friends 25 total people are going to buy ice cream cones. The set of all elements that that belong to either a or b or both is called the union of a and b denoted a. Sets, relations and binary operations set set is a collection of well defined objects which are distinct from each other. Two sets a and b are mutually exclusive or disjoint if they do not have any shared elements. The intersection of sets a and b is the set a\b fx. For example, the set of natural numbers is a subset of set of whole numbers which is a subset of integers. In a similar manner, there are several ways to create new sets from sets that have already been defined. There are more any set containing only elements that are also in a 3. Duplicates dont contribute anythi ng new to a set, so remove them. Basic definitions and concepts of set operations, relations.

Sets, relations and functions are the tools that help to perform logical and mathematical operations on mathematical and other realworld entities. In the next two chapters we will see that probability and statistics are based on counting the elements in sets and manipulating set operations. In fact, technically, a family of sets need not be a set, because we allow repeated elements, so a family is a multiset. Set operations and venn diagrams university of hawaii. Just as numbers can be compared via the relations greater than. The union of two sets is the set containing all of the elements from both of those sets. Bread a union b or the union of a and bis defined as the set that consists of all elements belonging to either set a or set b or both.

Two sets are said to be disjoint if their intersection is empty. The objects or symbols are called elements of the set. We will use capital letters for sets and lower case letters for elements. In the current worksheet, children are expected to look at each set of either number or entities and find the relationship or defining property of each.

Here are some examples of set operations and their venn diagrams. Write the set, n, of all letters in your first name. The order of the elements in a set doesnt contribute. Set theory for computer science university of cambridge. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. For any one of the set operations, we can expand to set builder notation, and then. A brief history of sets a set is an unordered collection of objects, and as such a set is determined by the objects it contains. For more practice exercises involving set operations, visit the companion web site and try the big operator. Union of sets a and b is defined to be the set of all those elements which belong to a or b or both and is denoted by a. We define two sets to be disjoint if their intersection is the empty set this means the two sets have no elements in common. The set t 2,3,1 is equal to s because they have the same members.

The notion of set is taken as undefined, primitive, or basic, so we dont try to define what a set is, but we can give an informal description, describe. Describe sets using either the verbal method or the roster method or the setbuilder method. Written \a\cup b\ and defined \a\cup b \x \mid x\in a\vee x\in b\\. While we usually list the members of a set in a standard order if one is available. You are without a car, but in need of a car next week. These are fundamental notions that will be used throughout the remainder of this text. Basic concepts of set theory, functions and relations. Sets in math are a collection of objects or numbers which have a common property. Sets and set operations sets computer science university at. Vowels in the english alphabet v a, e, i, o, u first seven prime. Families of sets when dealing with sets whose elements are themselves sets it is fairly common practice to refer to them as families of sets, however this is not a definition. Set operations and venn diagrams part 1 of 2 a venn diagram is a visual diagram that shows the relationship of sets with one another. With each number, place it in the appropriate region. Video for all operations of sets extra practiceinteractive links.

Set operations and the laws of set theory the union of sets a and b is the set ab fx. The standard query operator methods that perform set operations are listed in the following section. Some sets are bigger than others the cardinality of a set. One is to list them explicitly, like you would find in a database of names. Set operations two sets can be combined in many different ways. Sets, functions, relations northwestern university. The union of any two given sets a and b is the set c which consists of all those elements which are either in a. Discrete math study of the discrete structures used. The operation a b removes those members in set b that are in set a. The complement of a set a is the set of all elements in the universal set not contained in a, denoted a. Your pal adam is too busy studying and training to go out, and so he can loan you his car tuesday, wednesday, and thursday. Two sets are equal if and only if they have the same elements. A set is a welldefined collection of distinct objects. Sets and operations on sets mathematics libretexts.

Set operations union, intersection, complement solutions. A 1,2,3,6 b 2,4,6,9 a b 1,2,3,4,6,9 u a b cs 441 discrete mathematics for cs m. Sets help in distinguishing the groups of certain kind of objects. 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. The union of a1, a2, and an is the set that contains those elements that are members of at least one set. The venn diagram of a and b looks something like this. Locate all this information appropriately in a venn diagram. Shade the region of the venn diagram indicated by the following sets.

Video for interval notationset builder notationroster notation 2. There are two types of ice cream cones, chocolate and vanilla. The order of the elements in a set doesnt contribute anything new. We can represent this relationship through venn diagram in the following way. If xis a set and pis a property of elements of x, we denote the subset of x consisting of elements with the property pby fx2x.

A set is a well defined group of objects or symbols. For example, suppose that committee a, consisting of the 5 members jones, blanshard, nelson, smith, and hixon. In fact, technically, a family of sets need not be a. Union, intersection,cross product, difference and complement. These objects are sometimes called elements or members of the set. A set is a collection of objects, called elements of the set. Asetis acollection of objectsthat do not have an order. The set of all elements being considered is called the universal set u and is represented by a rectangle. Set theory, and set operations statistical science. In problems 11 16 that follow, the sets a, b, c and u are not the same sets that were used problems 1 10. Here is another set equality proof from class about set operations. The union of two sets is the set containing all of the elements from both of those sets written \a\cup b\ and defined \a\cup b \x \mid x\in a\vee x\in b\\. We use circles to represent the sets, and enclose our diagram in a rectangle. If 15 people buy vanilla cones, and 20 people buy chocolate cones, how many.