MHB Discrete Mathematics - Define a relation R on S of at least four order pairs

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A relation R on the set S = {1, 2, 5, 6} is defined by the condition that the product of the ordered pairs (a, b) is even. Valid pairs include (2, 1), (2, 5), (2, 2), (2, 6), (6, 1), (6, 5), and (6, 2), among others. The presence of the even number 2 or 6 in any pair ensures the product is even. The discussion emphasizes the importance of identifying pairs that satisfy this condition. Understanding such relations is crucial in discrete mathematics for analyzing properties of sets and their interactions.
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Let S = {1,2,5,6 }
Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)
 
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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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