1. The problem asks to translate logical quantifications involving the predicate $N(x)$, which means "x has visited New Delhi," where the domain is the students in your college. 2. The quantifiers used are: - $\exists x$: "There exists at least one x" - $\forall x$: "For all x" - $\sim$: negation "not" 3. Now, translate each statement: **a) $\exists x N(x)$** - This means "There exists at least one student x such that x has visited New Delhi." - In English: "At least one student in the college has visited New Delhi." **b) $\forall x N(x)$** - This means "For every student x, x has visited New Delhi." - In English: "Every student in the college has visited New Delhi." **c) $\sim \exists x N(x)$** - This means "It is not true that there exists a student who has visited New Delhi." - Equivalently, "No student in the college has visited New Delhi." **d) $\exists x \sim N(x)$** - This means "There exists at least one student x such that x has not visited New Delhi." - In English: "At least one student in the college has not visited New Delhi." **e) $\sim \forall x N(x)$** - This means "It is not true that all students have visited New Delhi." - Equivalently, "Not every student in the college has visited New Delhi." **f) $\forall x \sim N(x)$** - This means "For every student x, x has not visited New Delhi." - In English: "No student in the college has visited New Delhi." 4. Note that statements (c) and (f) are logically equivalent, both meaning no student has visited New Delhi. 5. Summary: - a) At least one student has visited New Delhi. - b) Every student has visited New Delhi. - c) No student has visited New Delhi. - d) At least one student has not visited New Delhi. - e) Not every student has visited New Delhi. - f) No student has visited New Delhi.