MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
Remember that two sets are
equal if and only if they have
exactly the same elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
∅ is the empty set. That means that it does not have ANY elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
∅ is the empty set. That means that it does not have ANY elements.
{ ∅ } is also the empty set.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
∅ is the empty set. That means that it does not have ANY elements.
{ ∅ } is also the empty set.is no longer empty.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
∅ is the empty set. That means that it does not have ANY elements.
{ ∅ } is also the empty set.is no longer empty.
An empty set, ∅, can’t be equal a set that is not empty, { ∅ }.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets ∅ and { ∅ } are equal.
∅ is the empty set. That means that it does not have ANY elements.
{ ∅ } is also the empty set.is no longer empty.
An empty set, ∅, can’t be equal a set that is not empty, { ∅ }.
The sets are NOT equal and the statement above is FALSE.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equal.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equal.
Remember that two sets are
equal if and only if they have
exactly the same elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equal.
It is easy to see here that these two sets do not
have exactly the same elements.
Remember that two sets are
equal if and only if they have
exactly the same elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equal.
It is easy to see here that these two sets do not
have exactly the same elements.
The sets are NOT equal and the statement above is FALSE.
Remember that two sets are
equal if and only if they have
exactly the same elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
{ 12 , 82 , 99 } and { a , e, p } are equivalent.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
{ 12 , 82 , 99 } and { a , e, p } are equivalent.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
{ 12 , 82 , 99 } and { a , e, p } are equivalent.
1
2
3
1
2
3
There are 3 elements in each set so the two sets are equivalent.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
{ 12 , 82 , 99 } and { a , e, p } are equivalent.
1
2
3
1
2
3
There are 3 elements in each set so the two sets are equivalent.
The statement above is TRUE.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equivalent.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equivalent.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equivalent.
1
2
3
4
5
1
2
3
4
5
There are 5 elements in each set so the two sets are equivalent.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equivalent.
1
2
3
4
5
1
2
3
4
5
There are 5 elements in each set so the two sets are equivalent.
The statement above is TRUE.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o} are equivalent.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o} are equivalent.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o} are equivalent.
1
2
3
4
5
1
2
3
4
There are 5 elements in one set and 4 in the other set
so the two sets are NOT equivalent.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o} are equivalent.
1
2
3
4
5
1
2
3
4
There are 5 elements in one set and 4 in the other set
so the two sets are NOT equivalent.
The statement above is FALSE.
Remember that two sets are
equivalent if they have the
same number of elements.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
{3, 4, 4, 5,
, 5, 66, 7, 7, 8, 8, 9,
, 9,10
10, 11,
, 11,12,
12,13
13} }
{3
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
{3, 4, 4, 5,
, 5, 66, 7, 7, 8, 8, 9,
, 9,10
10, 11,
, 11,12,
12,13
13} }
{3
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
{3, 4, 4, 5,
, 5, 66, 7, 7, 8, 8, 9,
, 9,10
10, 11,
, 11,12,
12,13
13} }
{3
Remember, the set of integers is the set of counting numbers
(the positive integers) plus the set of negative integers plus zero.
{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
{3, 4, 4, 5,
, 5, 66, 7, 7, 8, 8, 9,
, 9,10
10, 11,
, 11,12,
12,13
13} }
{3
Remember, the set of integers is the set of counting numbers
(the positive integers) plus the set of negative integers plus zero.
{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }
{3
{3, ,44, ,5,
5, 66, ,77, ,88, ,9,
9,10
10, ,11,
11,12,
12,13
13}}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False (Justify your answer.)
{𝑥: 𝑥 𝑖𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} and
{𝑦: 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 3 𝑎𝑛𝑑 13 𝑖𝑛𝑐𝑙𝑢𝑠𝑖𝑣𝑒} are equal.
{3, 4, 4, 5,
, 5, 66, 7, 7, 8, 8, 9,
, 9,10
10, 11,
, 11,12,
12,13
13} }
{3
Remember, the set of integers is the set of counting numbers
(the positive integers) plus the set of negative integers plus zero.
{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }
{3
{3, ,44, ,5,
5, 66, ,77, ,88, ,9,
9,10
10, ,11,
11,12,
12,13
13}}
This statement is TRUE.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
And we learned that the empty set (∅) is a subset of EVERY set.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
So this statement is TRUE.
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
And we learned that the empty set (∅) is a subset of EVERY set.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
So this statement is TRUE.
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
And we learned that the empty set (∅) is a subset of EVERY set.
∅ ⊂ {12 , 82 , 99}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
So this statement is TRUE.
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
And we learned that the empty set (∅) is a subset of EVERY set.
∅ ⊂ {12 , 82 , 99}
Set A is a proper subset of set B (written A ⊂ B)
if every element of A is also an element of B but A ≠ B.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
So this statement is TRUE.
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
And we learned that the empty set (∅) is a subset of EVERY set.
∅ ⊂ {12 , 82 , 99}
Set A is a proper subset of set B (written A ⊂ B)
if every element of A is also an element of B but A ≠ B.
We also learned that the empty set (∅) is a proper subset of EVERY set.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
True or False
∅ ⊆ {12 , 82 , 99}
So this statement is TRUE.
Set A is a subset of set B (written A ⊆ B)
if every element of A is also an element of B.
And we learned that the empty set (∅) is a subset of EVERY set.
∅ ⊂ {12 , 82 , 99}
This statement is also TRUE.
Set A is a proper subset of set B (written A ⊂ B)
if every element of A is also an element of B but A ≠ B.
We also learned that the empty set (∅) is a proper subset of EVERY set.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
1
2
3
4
5
6
7
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
1
2
3
4
5
6
7
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
So A has 27 = 𝟏𝟐𝟖 subsets
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
1
2
3
4
5
6
7
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
So A has 27 = 𝟏𝟐𝟖 subsets
How many proper subsets does A have?
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
1
2
3
4
5
6
7
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
So A has 27 = 𝟏𝟐𝟖 subsets
How many proper subsets does A have?
A proper subset of set A does not include A itself.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
1
2
3
4
5
6
7
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
So A has 27 = 𝟏𝟐𝟖 subsets
How many proper subsets does A have?
A proper subset of set A does not include A itself.
Therefore A has one less proper subset than 27
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
1
2
3
4
5
6
7
A = {11 , 12 , 13 , 14 , 15 , 17 , 18}
How many subsets does A have?
A set with k elements has 𝟐𝒌 subsets.
So A has 27 = 𝟏𝟐𝟖 subsets
How many proper subsets does A have?
A proper subset of set A does not include A itself.
Therefore A has one less proper subset than 27
So A has 27 = 128 − 1 = 𝟏𝟐𝟕 proper subsets
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Use the table to find the number of subsets of the set of
students who are either freshmen or athletes, or both.
MAJOR
CLASS RANK
GPA
ACTIVITIES
Gina
History
Freshman
3.8
Band
Dana
Biology
Freshman
1.4
Yearbook
Elston
Business
Freshman
1.7
Baseball
Frank
French
Senior
1.6
Soccer
Brenda
History
Junior
3.1
Tennis
Carmen
Business
Senior
3.7
Basketball
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Use the table to find the number of subsets of the set of
students who are either freshmen or athletes, or both.
MAJOR
CLASS RANK
GPA
ACTIVITIES
Gina
History
Freshman
3.8
Band
Dana
Biology
Freshman
1.4
Yearbook
Elston
Business
Freshman
1.7
Baseball
Frank
French
Senior
1.6
Soccer
Brenda
History
Junior
3.1
Tennis
Carmen
Business
Senior
3.7
Basketball
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Use the table to find the number of subsets of the set of
students who are either freshmen or athletes, or both.
MAJOR
CLASS RANK
GPA
ACTIVITIES
Gina
History
Freshman
3.8
Band
Dana
Biology
Freshman
1.4
Yearbook
Elston
Business
Freshman
1.7
Baseball
Frank
French
Senior
1.6
Soccer
Brenda
History
Junior
3.1
Tennis
Carmen
Business
Senior
3.7
Basketball
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Use the table to find the number of subsets of the set of
students who are either freshmen or athletes, or both.
MAJOR
CLASS RANK
GPA
ACTIVITIES
Gina
History
Freshman
3.8
Band
Dana
Biology
Freshman
1.4
Yearbook
Elston
Business
Freshman
1.7
Baseball
Frank
French
Senior
1.6
Soccer
Brenda
History
Junior
3.1
Tennis
Carmen
Business
Senior
3.7
Basketball
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Use the table to find the number of subsets of the set of
students who are either freshmen or athletes, or both.
So, there are 6
students who
are either
freshmen or
athletes (or both)
MAJOR
CLASS RANK
GPA
ACTIVITIES
Gina
History
Freshman
3.8
Band
Dana
Biology
Freshman
1.4
Yearbook
Elston
Business
Freshman
1.7
Baseball
Frank
French
Senior
1.6
Soccer
Brenda
History
Junior
3.1
Tennis
Carmen
Business
Senior
3.7
Basketball
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Use the table to find the number of subsets of the set of
students who are either freshmen or athletes, or both.
So, there are 6
students who
are either
freshmen or
athletes (or both)
MAJOR
CLASS RANK
GPA
ACTIVITIES
Gina
History
Freshman
3.8
Band
Dana
Biology
Freshman
1.4
Yearbook
Elston
Business
Freshman
1.7
Baseball
Frank
French
Senior
1.6
Soccer
Brenda
History
Junior
3.1
Tennis
Carmen
Business
Senior
3.7
Basketball
A set with 6 elements has 26 = 64 subsets
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
List all the subsets of the set given below.
2
1
3
A = {blackberry , blueberry , lemon}
Remember: A set with k elements has 𝟐𝒌 subsets.
So here, there are 23 = 8 subsets.
Let’s list them:
Subsets with:
0 elements
Ø
1 element
2 elements
3 elements
{blackberry} {blackberry, blueberry}
{blackberry, blueberry, lemon}
{blueberry} {blackberry, lemon}
{lemon}
{blueberry, lemon}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
A pizza place offers mushrooms, tomatoes and sausage as toppings for
a plain cheese base. How many different types of pizzas can be made?
The set of possible toppings is { M , T , S }
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
A pizza place offers mushrooms, tomatoes and sausage as toppings for
a plain cheese base. How many different types of pizzas can be made?
The set of possible toppings is { M , T , S }
Remember: A set with k elements has 𝟐𝒌 subsets.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
A pizza place offers mushrooms, tomatoes and sausage as toppings for
a plain cheese base. How many different types of pizzas can be made?
The set of possible toppings is { M , T , S }
Remember: A set with k elements has 𝟐𝒌 subsets.
Every subset of this set is a different pizza.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
A pizza place offers mushrooms, tomatoes and sausage as toppings for
a plain cheese base. How many different types of pizzas can be made?
The set of possible toppings is { M , T , S }
Remember: A set with k elements has 𝟐𝒌 subsets.
Every subset of this set is a different pizza.
So, there are
3
2 =8
different types of pizzas possible.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Amber wants to visit Dallas, Reno, Tulsa, Orlando, Atlanta, Nashville,
Phoenix, Mobile and Indianapolis. If she can decide to visit all, some
or none of these cities, how many travel options does Amber have?
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Amber wants to visit Dallas, Reno, Tulsa, Orlando, Atlanta, Nashville,
Phoenix, Mobile and Indianapolis. If she can decide to visit all, some
or none of these cities, how many travel options does Amber have?
The set of possible cities is {D,R,T,O,A,N,P,M,I}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Amber wants to visit Dallas, Reno, Tulsa, Orlando, Atlanta, Nashville,
Phoenix, Mobile and Indianapolis. If she can decide to visit all, some
or none of these cities, how many travel options does Amber have?
1
2
3
4
5
6
7
8
9
The set of possible cities is {D,R,T,O,A,N,P,M,I}
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Amber wants to visit Dallas, Reno, Tulsa, Orlando, Atlanta, Nashville,
Phoenix, Mobile and Indianapolis. If she can decide to visit all, some
or none of these cities, how many travel options does Amber have?
1
2
3
4
5
6
7
8
9
The set of possible cities is {D,R,T,O,A,N,P,M,I}
Remember: A set with k elements has 𝟐𝒌 subsets.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Amber wants to visit Dallas, Reno, Tulsa, Orlando, Atlanta, Nashville,
Phoenix, Mobile and Indianapolis. If she can decide to visit all, some
or none of these cities, how many travel options does Amber have?
1
2
3
4
5
6
7
8
9
The set of possible cities is {D,R,T,O,A,N,P,M,I}
Remember: A set with k elements has 𝟐𝒌 subsets.
Every subset of this set is a different travel option.
MATH 110 Sec 2-2: Comparing Sets
Practice Exercises
Amber wants to visit Dallas, Reno, Tulsa, Orlando, Atlanta, Nashville,
Phoenix, Mobile and Indianapolis. If she can decide to visit all, some
or none of these cities, how many travel options does Amber have?
1
2
3
4
5
6
7
8
9
The set of possible cities is {D,R,T,O,A,N,P,M,I}
Remember: A set with k elements has 𝟐𝒌 subsets.
Every subset of this set is a different travel option.
So, Amber has
29 =512
different travel options.