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Let $N(x)$ be the statements “$x$ has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English.

  1. $\exists x N(x)$
  2. $\forall x N(x)$
  3. $\sim \exists x N(x)$
  4. $\exists x \sim N(x)$
  5. $\sim \forall x N(x)$
  6. $\forall x \sim N(x)$

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1. $\exists x N(x)$

Some student has visited North Dakota

 

2. $\forall x N(x)$

All students have visited North Dakota

 

3. $\neg \  \exists x N(x)$

No student has visited North Dakota

 

4. $ \exists x \neg N(x)$

Some student has not visited North Dakota

 

5. $\sim \forall x N(x)$

Not all students have visited North Dakota

 

6. $\forall x \sim N(x)$

All students have not visited North Dakota
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a) there exists atleast one student in your school who has visited north dacota
b) every student in your school has visited north dacota
c) there doesnot exist even 1 student in your school who has visited north dacota
d) there exist atleast one student in your school who has not visited north dacota
e) not all students in your school has visited north dacota
f) all students in your class has not visited north dacota

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