Exercise 2. Words such as \"every\" and \"any\" normally correspond to universal

Question

Exercise 2. Words such as "every" and "any" normally correspond to universal quantifiers. However, the scope of the corresponding quantifier may depend on which is used. In this exercise, you are asked to consider an example which illustrates this point. Let the universe of discourse be the set of students in your class Let P(r) be "r passes the course" and let C be "we'll celebrate (a) In the sentence (var)P(z) C, (3) the scope of the quantifier (va) is just P(r). In the sentence (4) Copyright Neil Falkner 2016

Explanation / Answer

a) if everybody passes the exam , we'll celebrate corresponds to( for all x)P(x) => C

If anybody passes , we'll celebrate corresponds to for all x (P(x) => C)

b) it corresponds to the sentence that if anybody passes , we'll celebrate . i.e. to sentence 4

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