M8 L90 Introduction to Sets

Introduction to Sets

Math 8 Lesson 90

Set

A set is a collection of objects called elements.

Roster form is a way of listing the elements of a set using {}

Set

A set can be a collection of objects

Set

A set can be a collection of numbers

Multiple Choice

Using roster form, list the set of positive even intergers less than 10.

• {1,2,3,4,5,6,7,8,9,10}

• {1,2,3,4,5}

• {2,4,6,8,10}

• {2,4,6,8}

Multiple Choice

Using roster form, list the months with 31 days.

• {january, march, may, july, october, december}

• {january, march, may, july, august, october, december}

• {january, march, april, may, july, august, october, december}

• {january, march, april, may, july, august, september, october, december}

Null Set

The null or empty set is the set with no elements

Multiple Choice

Using roster form, list the months with 32 days.

• {january, march, may, july, october, december}

• {january, march, may, july, august, october, december}

• {february}

• { }

Elements

• An object in a set is called an element

• To show an element is a member of a set, we use a special symbol

Multiple Choice

What does the following mathematical statement mean? $$2\ \in the\ set\ of\ integers$$  

• 2 is a number

• 2 is an element of the set of integers

• 2 is rational

Multiple Choice

What does the following mathematical statement mean?  $$\frac{1}{2}\in the\ set\ of\ rational\ numbers$$

• 1/2 is a fraction

• 1/2 is an element of the set of rational numbers

• 1/2 is irrational

Multiple Choice

What does the following mathematical statement mean?

  $$\sqrt{2}\notin the\ set\ of\ rational\ numbers$$  

• the square root of 2 is a rational number

• the square root of 2 is not a rational number

• the square root of 2 is an  irrational number

Subsets

Multiple Select

Select all the true statements.

• $$A\subset B$$

• $$B\subset A$$

• $$1\in B$$

• $$5\notin A$$

What number sets are a subset of the set of real numbers?

Multiple Select

Select all the true statements.

• $$Q\subset R$$

• $$N\subset Q$$

• $$N\subset W$$

• $$R\subset Z$$

Multiple Select

Select all the true statements.

• $$2\in Z$$  

• $$0\in N$$  

• $$\frac{5}{3}\in Z$$  

• $$\pi\in R$$  

SET RELATIONSHIPS

The INTERSECTION of sets A and B is the set of all elements that are in BOTH A and B

The UNION of sets A and B is the set of all elements that are in EITHER A or B.

Intersection

Union

Multiple Choice

$$A\cup B$$  

• {2,4}

• {1,2,3,4}

• {1,2,3,4,6,8}

• {2,4,6,8}

Multiple Choice

$$A\cap B$$  

• {2,4}

• {1,2,3,4}

• {1,2,3,4,6,8}

• {2,4,6,8}

Multiple Choice

$$A\cap B$$  

• {2,4}

• {1,2,3,}

• {1,2,3,4,6,8}

• {1,2,3,4,...}

Multiple Choice

$$A\cup B$$  

• {2,4}

• {1,2,3}

• {1,2,3,4,6,8}

• {1,2,3,4,...}

Multiple Choice

$$A\cup B$$  

• {-3,-2,-1,1,2,. . .}

• {-1,-2,-3}

• {1,2,3,4,6,8}

• {1,2,3,4,...}

Multiple Choice

$$A\cap B$$  

• {-3,-2,-1,0,1,2,. . .}

• {-1,-2,-3}

• {  }

• {1,2,3,4,...}