Question

Write the following sentences in English, making clear what are the differences between them:

1. ∀ x ∃ y Class(x) ⇒ Student(y) ∧ In(y,x)

2. ∃ y ∀ x Student(y) ∧ Class(x) ⇒ In(y,x)

3. ∃ x ∃ y Class(x) ∧ Student(y) ∧ In(y,x)

4. ∀ x ∀ y Class(x) ∧ Student(y) ⇒ In(y,x)

5. ∀ x ∀ y Class(x) ∧ Student(y) ∧ In(y,x)

Answer 1

1. all class are students

2. there exists a student in class  

3.there exsits atleast one student in class

4. every student have class

5. every student have atleast one class

NOTE:

∀ x = Forall x

∃ y = there exsits y

∧ = And

⇒ = Implication

Check the truth table value of the notations and explain it in english