Math notes PDF

Preview

Summary

notes...

Description

A set can be described by: - Words - Roster method - Set-builder notation Words: - The set of seasons in a year - The set of days in a week - The set of letters of the English alphabet - The set of integers greater than -3 Roster Method: - List the elements of the set inside a pair of braces { } - Commas are used to separate the elements - 1. The set of seasons in a year {spring, summer, fall, winter} - 2. The set of days in a week {sun, mon, tues, wed, thurs, fri, sat} - 3. The set of letters in the English alphabet {a, b, c, d…} - 4. The set of integers greater than -3 {-2, -1, 0, 1, 2} Set Builder Notation: - The set of integers greater than -3 - 1. {X/X e I and X > -3} - The set of seasons in the year - 2. {X/X the set of seasons in a year} - The set of days in a week - 3. {X/X the set of days in a week} Examples: The set of natural numbers less than five {x/x e N and x < 5} The set of U.S coins with a value of less than fifty cents {x/x penny, nickel, dime, quarter} The solution set of x + 5 = -1 {x/x The set of months with exactly thirty days {x/x e September, April, June, November} The set of negative integers greater than -6 {x/x e I and X > -6}

The set of whole numbers less than 6 {x/x e w and x < 6} The set of natural numbers x that satisfy x + 4 = 1

The set of negative integers greater than or equal to -5 A set is finite if the number of elements in the se is a whole number The cardinal number of a finite set is the number of elements in the set, the cardinal number of finite set A is denoted by the notation n (A)

Equal Sets Set a is equal to set b, denoted by A=B, if and only if a and b have exactly the same elements Equivalent sets Set a is equivalent to set b, denoted by a ~ b, if and only if a and b have the same number of elements Universal set: the set of all elements that are being considered is called the universal set The complement of a set The complement of a set A, denoted by A’ is the set of all elements of the universal set U that are not elements of A Subset Set A is a subset of set b denoted by A c B if and only if every element of a is also an element of b Proper subset of a set Definition: set a is a proper subset of set b denoted by A c B. if every element of a is an element of b, then a does not equal b Intersection of sets The intersection of sets a and b denoted by a (n, upsidedown u) is the set of elements common to both a and b A (n, upsidedown u) B = {x|x E a and x E B} Union of sets The union of sets A and B denoted by A u B is the set that contains all the elements tha belong to A or to B or to both A u B = {x|x E a or x|x E b}

An element of U May be an element of both A and B. Region i May be an element of A but not B. Region ii May be an element of B but not A. Region iii May not be an element of either A or B. Region iv DeMorgan’s Law For all sets A and B (A u B)’ = A’ (n upsidedown u) B’ (A (n upsidedown u) B)’ = A’ U B’...