MHB How Do You Solve the Second Part of an Equivalence Relations Problem?

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The discussion focuses on understanding the second part of an equivalence relations problem after establishing that the first part meets the criteria of reflexivity, symmetry, and transitivity. A user seeks clarification on how to approach this second part, indicating confusion regarding the problem statement. Other participants encourage providing more details about the specific problem to facilitate better assistance. The conversation emphasizes the importance of clearly defining the problem to solve it effectively. Overall, the thread highlights the need for collaborative problem-solving in mathematical contexts.
loydchase
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I understand that the first part of the equation is an equivalence class due to reflexivity, symmetry, and transivity... but I am confused on the second part. Could someone please help me out? THANKS
 
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What exactly is the problem statement?
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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