Anavi A.

asked • 05/10/21

Explain quantifications in English

How would you describe each of these quantifications in English?

a) ∃x¬Z(x)

b) ¬∀xZ(x)

Where Z(x)=“x has spent a quiet evening at home,” , Domain = Ali’s friends

Inactive Tutor

The most intuitive way to approach this is to do what I call the "google translate method" (trademark, me haha). Just have a set "translation" for each symbol. Then, put it together. After doing that, it might not make perfect sense, but then you can polish it to make it more understandable. For example: ∃ = "there exist(s)", ¬ = "not", ∀ = "for all" : = "such that" Then given and Z(x,y) = "x is the twin of y", you can translate ∀y ¬∃x: Z(x,y) as: "For all y, not exist x such that x is the twin of y." Then looking at this sentence you can see that this is saying that for all people (represented by y), there is not another person x that is there twin. In other words, there isn't anyone who is the twin of someone else (of course this statement is not true, but the statement says it). Try it out and see if that helps!
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06/18/21

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