Subsets and Proper Subsets

Subsets and Set Operations

Lesson objective

To Define Subsets and Perform Set Operations 

Set Operations

• Subsets and Proper Subsets

• (Intersection and Union) of Sets

• Set Subtraction (Difference of Sets)

Multiple Choice

............................................ :

The set of all objects that are reasonable to consider in a situation.

• Universal Set (U)

• Venn Diagram

• Set Operation

• Disjoint Sets

• Difference of Sets

  (set subtraction)

Multiple Choice

............................................ :

A method for visualizing sets and their relationships.

• Universal Set (U)

• Venn Diagram

• Set Operation

• Disjoint Sets

• Difference of Sets

  (set subtraction)

Multiple Choice

............................................ :

The set of elements in the universal set that are not in A. All the things inside the rectangle that are not inside the circle representing set A. A’ = { x | x ∈ U and x ∉ A }.

• Complement of a set A (A’)

• A is a Subset of b (A⊆B)

• A is a Proper Subset of B (A⊂B)

• Intersection (A∩B) (and)

• Union (A∪B) (Or)

Multiple Choice

In the following Venn diagram, the universal set U is:

• {1, 2, 3, 4, 5, 6, 7, 8}

• {2, 4, 6, 8}

• {1, 3, 5, 7}

• { }

Multiple Choice

In the following Venn diagram, the set A is:

• {1, 2, 3, 4, 5, 6, 7, 8}

• {2, 4, 6, 8}

• {1, 3, 5, 7}

• { }

Multiple Choice

In the following Venn diagram, the complement of the set A (A') is:

• {1, 2, 3, 4, 5, 6, 7, 8}

• {2, 4, 6, 8}

• {1, 3, 5, 7}

• { }

Multiple Choice

Let U = {10, 20, 30, 40, 50, 60, 70, 80, 90} and A = {10, 30, 50}. Find A'.

• {10, 20, 30, 40, 50, 60, 70, 80, 90}

• {10, 20, 30}

• {10, 30, 50}

• {20, 40, 60, 70, 80, 90}

Multiple Choice

What is the complement of the empty set?

• The Universal Set

• The Set A

• Any set

• { }

Multiple Choice

............................................ :

If every element of a set A is also an element of a set B. if there are no elements in A that are not also in B. When one set is contained in a second set, we call the smaller set a subset of the larger one.

• Complement of a set A (A’)

• A is a Subset of b (A⊆B)

• A is a Proper Subset of B (A⊂B)

• Intersection (A∩B) (and)

• Union (A∪B) (Or)

Multiple Choice

Decide whether the statement is True or False.

Every set is a subset of itself.

Every element of a set A is an element of set A. So, A⊆A.

• True

• False

Multiple Choice

Decide whether the statement is True or False.

The empty set is a subset of every set.

The empty set has no elements, so for any set A, you can’t find an element of ∅ that is not also in A.

• True

• False

Multiple Select

For the set {x, y, z}, Select all the subsets we can form.

• {x}, {y}, {z}

• {x, y}, {x, z}, {y, z}

• {x, y, z}

• ∅

Multiple Select

Find all subsets of B = {Laptop, Mobile, Tv}

• {Laptop}, {Mobile}, {Tv}

• {Laptop, Mobile}, {Laptop, Tv}, {Mobile, Tv}

• {Laptop, Mobile, Tv}

• ∅

Multiple Choice

............................................ :

If a set A is a subset of a set B and is not equal to B. That is, A⊆B and A ≠ B.

• Complement of a set A (A’)

• A is a Subset of b (A⊆B)

• A is a Proper Subset of B (A⊂B)

• Intersection (A∩B) (and)

• Union (A∪B) (Or)

Multiple Select

Find all proper subsets of B = {Laptop, Mobile, Tv}

• {Laptop}, {Mobile}, {Tv}

• {Laptop, Mobile}, {Laptop, Tv}, {Mobile, Tv}

• {Laptop, Mobile, Tv}

• ∅

Multiple Choice

Decide if the statement is True or False.

{8} ⊆ {x | x is an even natural number}

• True

• False

Multiple Choice

Decide if the statement is True or False.

{6} ⊆ {1, 3, 5, 7, . . .}

• True

• False

Multiple Choice

Decide if the statement is True or False.

{2, 3} ⊆ { x | x ∈ N}

• True

• False

Multiple Choice

Decide if the statement is True or False.

{a, b, c} ⊂ {letters of the alphabet}

• True

• False

Multiple Choice

Decide if the statement is True or False.

∅ ∈ {x, y, z}

• True

• False

Multiple Choice

Decide if the statement is True or False.

∅ ⊆ {red, yellow, blue}

• True

• False

Multiple Choice

Decide if the statement is True or False.

{∅} ⊆ ∅

• True

• False

Multiple Choice

Decide if the statement is True or False.

{100, 200, 300, 400} ⊂ {200, 300, 400}

• True

• False

Multiple Choice

If a finite set has n elements, then the set has 2^n subsets and 2^n − 1 proper subsets.

• True

• False

Multiple Choice

Find the number of subsets of the set {OSU, USC, KSU, MSU, UND, PSU, UT, FSU}

• 2

• 8

• 16

• 256

• 255

Multiple Choice

Find the number of proper subsets of the set {OSU, USC, KSU, MSU, UND, PSU, UT, FSU}

• 2

• 8

• 16

• 256

• 255

Multiple Choice

............................................ :

A rule for combining two or more sets to form a new set.

• Universal Set (U)

• Venn Diagram

• Set Operation

• Disjoint Sets

• Difference of Sets

  (set subtraction)

Multiple Choice

............................................ :

The set of all elements that are in both sets. Objects that are common to two or more sets. A∩B = { x | x ∈ A and x ∈ B }.

• Complement of a set A (A’)

• A is a Subset of b (A⊆B)

• A is a Proper Subset of B (A⊂B)

• Intersection (A∩B) (and)

• Union (A∪B) (Or)

Multiple Choice

............................................ :

The set of all elements that are in either set A or set B or both. A∪B = { x | x ∈ A or x ∈ B }.

• Complement of a set A (A’)

• A is a Subset of b (A⊆B)

• A is a Proper Subset of B (A⊂B)

• Intersection (A∩B) (and)

• Union (A∪B) (Or)

Multiple Choice

If A = {10, 12, 14, 15} and B = {13, 14, 15, 16, 17}, then the intersection A ∩ B =

• {10, 12, 14, 15}

• {13, 14, 15, 16, 17}

• {10, 12, 13, 14, 15, 16, 17}

• {14, 15}

• {10, 12, 13, 16, 17}

Multiple Choice

If A = {10, 12, 14, 15} and B = {13, 14, 15, 16, 17}, then the intersection A ∪ B =

• {10, 12, 14, 15}

• {13, 14, 15, 16, 17}

• {10, 12, 13, 14, 15, 16, 17}

• {14, 15}

• {10, 12, 13, 16, 17}

Multiple Choice

............................................ :

When the intersection of two sets is the empty set. If the sets have no elements in common.

• Universal Set (U)

• Venn Diagram

• Set Operation

• Disjoint Sets

• Difference of Sets

  (set subtraction)

Multiple Choice

............................................ :

The set of elements in set A that are not in set B. A-B = { x | x ∈ A and x ∉ B }.

• Universal Set (U)

• Venn Diagram

• Set Operation

• Disjoint Sets

• Difference of Sets

  (set subtraction)

Multiple Choice

A = {18,19,20,21,22}, B = {22,23,24} and C = {17,18,19}. Find A−C.

• {18,19,20,21,22}

• {18,19,20,21}

• {20,21,22}

• {17, 18,19,20,21,22}

Poll

Are you confident about our lesson Today?

• Very confident

• Somewhat confident

• Little confident

• Not confident

The End

Thank You :)