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More Lessons On Sets
Universal Set
Venn Diagrams
In these lessons, we will learn the concept of subsets and proper subsets and the formula for the number of subsets in a finite set.
Sets & Set Notations | ||
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Subsets & Proper Subsets | Number of Subsets Formula | Subset Video Lessons |
If every member of set A is also a member of set B, then A is a subset of B, we write A ⊆ B. We can say A is contained in B.
We can also say B ⊇ A, B is a superset of A, B includes A, or B contains A.
If A is not a subset of B, we write A ⊈ B.
If A is a subset of B (A ⊆ B), but A is not equal to B, then we say A is a proper subset of B, written as A ⊂ B or A ⊊ B.
The following diagram shows an example of subset. Scroll down the page for more examples and solutions on subsets.
Example:
A = {1, 3, 5}, B = {1, 2, 3, 4, 5}, C = {1, 2, 3, 4, 5}
A is a subset of B, A ⊆ B. because every element in A is also in B
A is also proper subset of B, A ⊂ B. because every element in A is also in B and A ≠ B
C is subset of B, C ⊆ B. but is not a proper subset of B because C = B
Example:
X = {1, 3, 5}, Y = {2, 3, 4, 5, 6}.
X is not a subset of Y, X ⊈ Y, because the element 1 is in X but not in Y.
Note:
Example:
List all the subsets and proper subsets of the set Q = {x, y, z}
Solution:
The subsets of Q are { }, {x}, {y}, {z}, {x, y}, {x, z}, {y, z} and {x, y, z}
The proper subsets of Q are { }, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}
The number of subsets for a finite set A is given by the formula:
If set A has n elements, it has 2^{n} subsets.
If set A has n elements, it has 2^{n} - 1 proper sets.
Example:
Q = {x, y, z}. How many subsets and proper subsets will Q have?
Solution:
Q has 3 elements
Number of subsets = 2^{3 }= 8
Number of proper subsets = 7
Example:
Draw a Venn diagram to represent the relationship between the sets. A = {1, 3, 5} and B = {1, 2, 3, 4, 5}
Solution:
Since A is a subset of B:
Step 1: Draw circle A within the circle B
Step 2: Write down the elements in circle A.
Step 3: Write down the remaining elements in circle B
Subset Worksheets
Distinguish between subsets and proper subsets. Find the number of subsets in a given set.
Sets Worksheets
More Worksheets for Sets
This video defines and give the notation or symbols used for subsets and proper subsets and shows how to determine the number of possible subsets for a given set.
How do we find the number of subsets a set has? How many subsets does any given set has? In this video we go over some example problems, calculating the number of subsets a set has.
If a set has n elements then it has 2^{n} subsets.
Example:
Indicate whether true or false:
{} ⊆ {2, 3}
{} ∈ {2, 3}
{} ∈ {{}, 2, 3}
{5, 6, 7} ⊆ {5, 6, 7, 8}
{5, 6, 7, 8} ⊆ {5, 6, 7, 8}
{5, 6, 7, 8} ⊂ {5, 6, 7, 8}
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