# Set Theory: Equal and Equivalent Sets

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

Related Topics: More Lessons on Sets

## Equal 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.

## Equivalent Sets

Two sets are

equivalent if they have the same number of elements.

Equal and Equivalent Sets

An explanation of equal sets, equivalent sets, one-to-one correspondence and cardinality.