MHB Can I Determine if a Formula is a Tautology by Finding its CNF and DNF?

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To determine if a formula is a tautology, one can find its Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF). The discussion highlights that the solution process can be challenging, and it is suggested to use $\LaTeX$ for clarity in presenting formulas. Additionally, posting images in full size rather than as thumbnails is recommended for better accessibility. The conclusion confirms that the formula in question is indeed a tautology. Understanding CNF and DNF is essential for evaluating the truth of logical formulas.
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find cnf and dnf
 
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my solution can't go far
 
It would be better if you used $\LaTeX$ or at least posted the images not as thumbnails, but full sized so people don't have to click on them, opening up a new tab. :D
 
This formula is a tautology.
 

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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