### About Sets Part 1:

A set is a collection of things in which the order is not important. We enclose the items or elements of a set with curly braces: “{}”. We name sets with capital letters such as A, B, or K. We can say set A is the set of whole numbers that are even and less than 12: A = {0, 2, 4, 6, 8, 10}.

Test Objectives

- Demonstrate the ability to list the elements of a set using the roster method
- Demonstrate the ability to determine if one set is a subset of another
- Demonstrate the ability to determine if a particular element belongs to given set

#1:

Instructions: List the elements of each set using the roster method.

a) The set of all whole numbers less than 9

b) The set of states that border Idaho

c) The set of oceans on planet earth

d) The set of female presidents of the U.S.

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#2:

Instructions: List the elements of each set using the roster method.

a) The set of all integers between -3 and 4

b) The set of letters of the alphabet between "a" and "b"

c) The set of all even integers larger than 2

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#3:

Instructions: Determine if each statement is true or false.

A = {3,7,5} : B = {6,2,1}

C = {1,2,3,4,5,6,7,8,9,10,11}

a) 6 ∈ A

b) 10 ∈ C

c) 2 ∉ B

d) B ⊂ A

e) A ⊂ C

f) B ⊂ C

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#4:

Instructions: Determine if each statement is true or false.

A = {a,c} : B = {d,e}

C = {a,b,c,d,e,f,g,h}

D = {n,p} : E = {a,e}

a) n ∈ D

b) p ∉ B

c) a ∈ A

d) e ∉ C

e) B ⊂ C

f) A ⊂ D

g) A ⊂ E

h) E ⊂ C

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#5:

Instructions: Determine the number of subsets that can be made from each set, then list the subsets.

a) A = {1,8,7,5}

b) D = {a,e,o}

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Written Solutions:

#1:

Solutions:

a) {0, 1, 2, 3, 4, 5, 6, 7, 8}

b) {Utah, Nevada, Oregon, Washington, Montana}

c) {Pacific, Atlantic, Indian, Southern, Arctic}

d) { } or Ø

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#2:

Solutions:

a) {-2, -1, 0, 1, 2, 3}

b) { } or Ø

c) {4, 6, 8, 10, 12,...}

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#3:

Solutions:

a) false

b) true

c) false

d) false

e) true

f) true

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#4:

Solutions:

a) true

b) true

c) true

d) false

e) true

f) false

g) false

h) true

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#5:

Solutions:

a) 16 : {1}, {8}, {7}, {5}, {1,8}, {1,7}, {1,5}, {8,7}, {8,5}, {7,5}, {1,8,7}, {1,7,5}, {8,7,5}, {1,8,5}, {1,8,7,5}, Ø

b) 8 : {a}, {e}, {o}, {a,e}, {a,o}, {e,o}, {a,e,o}, Ø