Set Theory: Equal and Equivalent Sets
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
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 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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