Here are the conclusions for each statement:

1. Conclusion: ∀n ∈ ℕ (n + 1 > n), where n is a natural number.
2. Conclusion: ∃p ∈ P (p is even), where p is a prime number.
3. Conclusion: ∃x (M(x) ∧ L(x)), where M(x) means "x is a mammal" and L(x) means "x gives live birth."
4. Conclusion: ∃x (B(x) ∧ F(x)), where B(x) means "x is a bird" and F(x) means "x can fly."
5. Conclusion: ∀x (S(x) → P(x)), where S(x) means "x is a student" and P(x) means "x passed the exam."
6. Conclusion: ∃x (C(x) ∧ ¬S(x)), where C(x) means "x is a city" and S(x) means "it snows in x."
7. Conclusion: ∀x ∈ ℤ (x² ≥ 0), where x is an integer.
8. Conclusion: ∃x (L(x) ∧ ¬C(x)), where L(x) means "x is a language" and C(x) means "x is spoken in every country."
9. Conclusion: ∀x (E(x) → T(x)), where E(x) means "x is an employee" and T(x) means "x is required to complete a training program."
10. Conclusion: ∃x (S(x)), where S(x) means "x is a solution to the equation."

Let me know if you'd like further details or explanations for any of the steps!

Here are some follow-up questions:

1. What do negations mean in formal logic?
2. Can you explain the significance of quantifiers like ∀ and ∃?
3. How do you form negations for mathematical statements?
4. What are the differences between the symbols ∧ (and) and ∨ (or)?
5. How do you apply logic to real-world scenarios using mathematical statements?

Tip: When negating statements in formal logic, pay attention to the quantifiers. Negating an existential quantifier (∃) changes it to a universal quantifier (∀) and vice versa.