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dpa
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Homework Statement
A solution to a problem has following operation:
here, [(a,b)] and [(m,n)] are two equivalence classes.
[(a,b)]+[(m,n)]=[(an+bm,bn)]
Is not
[(a,b)]+[(m,n)]=[(a+m,b+n)]?
Can anyone explain it to me?
You can define "sum of equivalence classes" to be whatever you want as long as it is "well defined". This sum might be "well defined" for a different equivalence relation. What equivalence relation are you working with?[(a,b)]+[(m,n)]=[(a+m,b+n)]
An equivalent class in an operation is a set of elements that produce the same result when the operation is applied to them. This means that all elements in an equivalent class are interchangeable and can be considered equal in terms of the operation being performed.
To determine equivalent classes in an operation, you need to identify which elements produce the same result when the operation is applied to them. This can be done by comparing the output of the operation for different elements or by using mathematical properties of the operation.
Understanding equivalent classes in an operation is important because it helps us better understand the behavior and properties of the operation. It also allows us to simplify complex operations by grouping elements into equivalent classes, making calculations and problem-solving easier.
Yes, equivalent classes can change in different operations. The concept of equivalent classes is specific to a particular operation, so it can vary depending on the operation being performed. Different operations may have different ways of determining equivalent classes and may produce different results.
Equivalent classes can be used in real-world applications in various fields such as computer science, mathematics, and engineering. They can help in data classification and organization, optimization of algorithms, and problem-solving. For example, in computer programming, equivalent classes can be used to group similar data or code and improve the efficiency of the program.