In these lessons, we will learn

If every element of a set*B* is also a member of a set *A*, then we say *B* is a **subset** of *A*. We use the symbol ⊂to mean "is a subset of" and the symbol ⊄ to mean "is not a subset of

Example:

*A* = {1, 3, 5}, *B* = {1, 2, 3, 4, 5}

List all the 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*}

Example:

*Q* = {*x, y, z*}. How many subsets will *Q* have?
Solution:

n(*Q*) = 3

Number of subsets = 2^{3 }= 8

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 and Proper Subset

This video defines and give the notation used for subsets and proper subsets.
Learn about subset and proper subset.

Number of Subsets.
Subsets of the Real Number System

Brief description of the set of real numbers and its subsets: naturals, wholes, integers, rationals, and irrationals.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- about subsets and proper subsets
- the formula for the number of subsets

If every element of a set

Example:

So, *A *⊂ *B* because every element in *A* is also in *B.*

*X* = {1, 3, 5}, *Y* = {2, 3, 4, 5, 6}.

*X *⊄ *Y *because 1 is in *X* but not in *Y.*

*Note**:*

- Every set is a subset of itself i.e. for any set
*A, A*⊂*A* - The empty set is a subset of any set
*A*i.e. ∅ ⊂*A* - For any two sets
*A*and*B*, if*A*⊂*B*and*B*⊂*A*then*A*=*B*

List all the subsets of the set

The subsets of

The number of subsets for a finite set *A* is given by the formula:

Number of subsets = 2

^{ n(A)}where n(

A) = number of elements in the finite setA

Example:

n(

Number of subsets = 2

Example:

Draw a Venn diagram to represent the relationship between the sets.

Solution:

Since

Step 1: Draw circle

Step 2: Write down the elements in circle

Step 3: Write down the remaining elements in circle

This video defines and give the notation used for subsets and proper subsets.

Brief description of the set of real numbers and its subsets: naturals, wholes, integers, rationals, and irrationals.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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