Subsets and Proper Subsets

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

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A method for visualizing sets and their relationships.

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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 }.

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

In the following Venn diagram, the set A is:

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

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

What is the complement of the empty set?

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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.

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.

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.

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

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

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

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

Decide if the statement is True or False.

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

Decide if the statement is True or False.

{6} ⊆ {1, 3, 5, 7, . . .}

Decide if the statement is True or False.

{2, 3} ⊆ { x | x ∈ N}

Decide if the statement is True or False.

{a, b, c} ⊂ {letters of the alphabet}

Decide if the statement is True or False.

∅ ∈ {x, y, z}

Decide if the statement is True or False.

∅ ⊆ {red, yellow, blue}

Decide if the statement is True or False.

{∅} ⊆ ∅

Decide if the statement is True or False.

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

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

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

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

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

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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 }.

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

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

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

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

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

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

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