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

**Related Pages**

Describing Sets

Set Notation

Venn Diagrams And Subsets

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 5x ≤ 15}

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

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

**Solution:**

5x ≤ 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**

**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?**

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