Table of Contents
Equivalent Set and its Significance
Equivalent set is a set that has the same cardinality as another set. In other words, the two sets have the same number of elements. The significance of equivalent sets is that they can be used to represent other sets. For example, if you are given a set of numbers, you can represent it using an equivalent set. This can be helpful when you are trying to solve a problem or when you are trying to understand a concept.
Equivalent Set Definition
An equivalence relation is a binary relation that is reflexive, symmetric, and transitive.
Reflexive : For all a in A, aRb if and only if a=b.
: For all a in A, aRb if and only if a=b. Symmetric : For all a,b in A, aRb if and only if bRa.
: For all a,b in A, aRb if and only if bRa. Transitive: For all a,b,c in A, aRb and bRc if and only if a=c.
Equal Set
If we take two sets, A and B, and consider them to be equal, then this means that every element in A is also an element in B, and vice versa. In other words, the sets are identical. Symbolically, we can write this as:
A = B
This equality can be tested mathematically, by checking to see if the two sets have the same size (that is, if they have the same number of elements).
Equal Set Example
We can use the equal set operator to create a set of all the integers that are equal to 7.
The set {7} is created.
Symbol of Equal Set
The symbol of an equal set is two parallel lines.
Equivalent Set Example
{1, 2, 3}
The equivalent set is {1, 2, 3, 4, 5}.
Equivalent Sets Symbol
A set of all real numbers
A set of all natural numbers
A set of all rational numbers
A set of all irrational numbers
A set of all positive real numbers
A set of all negative real numbers
Relation Between Equal and Equivalent Sets
A set is equal to another set if and only if the two sets have the same elements. A set is equivalent to another set if and only if the two sets have the same cardinality.
:
I was very pleased with the quality of the product and the ease of the installation.
5 out of 5 stars Comfort
5 out of 5 stars Quality
5 out of 5 stars Value
5 out of 5 stars Installation
5 out of 5 stars Reliability
Purchased on Dec 21, 2016
Reviewed on Feb 8, 2017
I was very pleased with the quality of the product and the ease of the installation.
5 out of 5 stars Comfort
5 out of 5 stars Quality
5 out of 5 stars Value
5 out of 5 stars Installation
5 out of 5 stars Reliability
Purchased on Dec 21, 2016
Reviewed on Feb 8, 2017
I was very pleased with the quality of the product and the ease of the installation.
5 out of 5 stars Comfort
5 out of 5 stars Quality
5 out of 5 stars Value
5 out of 5 stars Installation
5 out of 5 stars Reliability
Purchased on Dec 21, 2016
Reviewed on Feb 8, 2017
I was very pleased with the quality of the product and the ease of the installation.
5 out of 5 stars Comfort
5 out of 5 stars Quality
5 out of 5 stars Value
5 out of 5 stars Installation
5 out of 5 stars Reliability
Purchased on
