In these lessons, we will learn about equal sets and equivalent sets.

Related Topics: More Lessons on Sets

### Equal Sets

Learn about equal sets.

**Equal sets, equivalent sets, one-to-one correspondence and cardinality**

Two sets are equivalent if they have the same number of elements.

The elements do not need to be the same.

Equivalent sets have one-to-one correspondence to each other.

The cardinality of a set is the number of elements in the set.
**What are Equivalent Sets?**

You can use the free Mathway calculator and problem solver 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.

Related Topics: More Lessons on Sets

Two sets, *P* and *Q*, are **equal sets** if they have exactly the same members. Each element of *P* are in *Q* and each element of *Q* are in *P*. The order of elements in a set is **not** important.

**Example :**

List the elements of the following sets and show that *P* ≠ *Q*
and *Q* = *R*.

* P* = {*x* : *x* is a positive integer and 5*x* ≤ 15}

* Q* = {*x* : *x* is a positive integer and *x* 2 < 25}

*R* = {*x* : *x* is a positive integer and *x *≤ 4}

**Solution : **

5*x* ≤ 15 ⇒ *x* ≤ 3 So,* P* = {1, 2, 3}

* x* ^{2} < 25 ⇒ *x* < 5 So, * Q* = {1, 2, 3, 4}

* R* = {1, 2, 3, 4}

Therefore, *P* ≠ *Q* and *Q* = *R*.

Learn about equal sets.

Two sets are equivalent if they have the same number of elements.

The elements do not need to be the same.

Equivalent sets have one-to-one correspondence to each other.

The cardinality of a set is the number of elements in the set.

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You can use the free Mathway calculator and problem solver 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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