- #1
shivajikobardan
- 674
- 54
- Homework Statement
- Confusions about finding equivalence classes for the set of natural numbers corresponding to equivalence relation a+b is even.
- Relevant Equations
- N/A
##a \in N##, but what set does b belong to?##R = \{(a, b) : (a + b) \text{ is even} \}##
What is set A? You haven't defined it, so there's no way to determine whether an element x belongs to A or not.##[a] = \{x | x \in A \land (a, x) \in R \}##
Mark44 said:Your conclusion that ##[0] \equiv [2] \equiv [4] \dots \equiv[2n] = \{2, 4, 6, 8, \dots \}## looks OK to me, and similar for ##[1]\equiv [3] \equiv [5] \dots \equiv[2n + 1] = \{1, 3, 5, 7, \dots \}##.
There are several things in what you wrote that are unclear, though.
I thought ##R=\left\{(a,b):a+b~~ is ~~even\right\} ##Mark44 said:##a \in N##, but what set does b belong to?
That part is definition part. My bad I put there (thought it would be useful but turned out opposite). Here A=N in my question. It is the given set.Mark44 said:What is set A? You haven't defined it, so there's no way to determine whether an element x belongs to A or not.
Equivalence classes confusions refer to a common issue in scientific research where different groups or categories are mistakenly considered to be equivalent, leading to incorrect conclusions or interpretations.
Equivalence classes confusions can occur when researchers fail to properly define and distinguish between different groups or categories in their study, leading to incorrect assumptions about their similarities or differences.
The consequences of equivalence classes confusions can be significant, as they can lead to incorrect conclusions, biased results, and a waste of time and resources in research efforts.
To avoid equivalence classes confusions, researchers should thoroughly define and differentiate between groups or categories in their study, and use appropriate statistical methods to analyze and compare them.
In some cases, equivalence classes confusions can be corrected by re-analyzing data with a more accurate understanding of the different groups or categories involved. However, prevention is always the best approach in scientific research.