Understanding Universal vs. Existential Quantifiers in Relationships

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The discussion centers on the interpretation of the phrase "any person who LOVES a SLOB is him(her)self a SLOB" in terms of quantifiers. One participant argues that it involves an existential quantifier due to the use of "a slob," suggesting it refers to at least one slob. Conversely, another participant contends that the phrase should be understood with a universal quantifier, indicating a broader application to all individuals who love slobs. The debate highlights the complexity of quantifier representation in language and its implications in relationships. Ultimately, the conversation emphasizes the need for clarity in distinguishing between universal and existential quantifiers.
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Any person who LOVES a SLOB is him(her)self a SLOB.

In this sentence does "any person who loves a slob.." involve a universal quantifier for the slob or a existential quantifier? I think its existential since it says "a slob"
 
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Show how you are representing the sentence. What variable are you assigning a qualifier to?

I think the textbook answer to this sentence involves only a universal quantifier.
 

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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