Sets and Venn Diagrams

Z or Integers

{ ...-3, -2, -1, 0, 1, 2, 3...}

W or Whole numbers

{ 0,1,2,3,4,5...}

N or Natural numbers

{ 1,2,3,4,5...}

INFINITE SET

a set with an infinite number of elements for example, the set of all even numbers { 2,4,6,8...}

SET BUILDER NOTATION

a way to describe sets of numbers

UNION

all elements which are in P OR Q

INTERSECTION

all elements which are in both set P AND set Q

I or Irrational numbers

all numbers that are not rational numbers, also called Q' (or not Q) like pi or square root of 2

ELEMENT

an object in a set, also called a member

MEMBER

an object in a set, also called an element

CLOSED CIRCLE ON A NUMBER LINE

numbers are included in a set <= and >= sign (less than or equal to, greater than or equal to)

OPEN CIRCLE ON A NUMBER LINE

numbers not included in a set < and > sign (less than, greater than)

Q or Rational numbers

numbers that can be written as a fraction where the numerator and the denominators are both integers and the denominator is NOT 0

n(S)

read as the number of elements in a set if D= {2,3,4,5,6,7,8,9,} then the n(D)=8

VENN DIAGRAM

represented by a rectangle represents the Universal Set the sets within are represented by circles

Z-

set of all negative integers

R or Real numbers

the set of all rational and irrational numbers

UNIVERSAL SET

the set of objects under consideration

MUTUALLY EXCLUSIVE SETS

two sets with absolutely nothing in common, also called disjoint

DISJOINT SETS

two sets with absolutely nothing in common, also called mutually exclusive

SUBSET

Every element of P is also an element of Q. For example if I tell you that Q = {1,2,3,4,5,6}, P ={2,4,6} and R ={2,4,6,8} then P is a subset of Q but R is not a subset of Q because 7 is not in Q

Z+

set of all positive integers

COMPLEMENT

the elements that are NOT in the stated set Example: A' is read ''complement of A'' and means all the elements that are NOT in A

EMPTY SET

A set with no elements { }

SET

a collection of objects or things

FINITE SET

a set with a given number of elements for example, the set of the outcomes when rolling a dice { 1,2,3,4,5,6}