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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 PQ 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, PQ 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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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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