Work out the following problem by hand and prove the following. Upload a photo of your work. \( \exists x , \quad Ka \quad \therefore \quad \exists x (Bx \land x = a) \)

Work out the following problem by hand and show that each of the following arguments is valid using a natural deduction proof in FOL. Upload a photo of your work. \( \forall x (Lx \rightarrow Gx), \quad \exists x Lx \quad \therefore \quad \exists x Gx \)

Evaluate the limit  first by using techniques from Chapter 1 then by using L’Hopital’s Rule. ​

True or False: The function  is one-to-one on its entire domain. ​

According to Tocqueville, which of the following is an inevitable source of dogmatic belief in every society?

For Nietzsche, all human meaning takes the form of:

What is Nietzsche’s critique of the rationalism of the Enlightenment?

What was Marx’s critique of bourgeois morality and bourgeois freedom?

What is Rousseau’s political solution to the problem of modern civilization?

Which of the following best represents John Stuart Mill’s position regarding moral truth?