Let F be a field and suppose that P is a subset of F that satisfies the three properties in Exercise 8. Define x ∈ P. Prove that “ Exercise 8 Let P = {x ∈ R: x > 0}. Show that P satisfies the...

Let F be a field and suppose that P is a subset of F that satisfies the three properties in Exercise 8. Define x <>∈ P. Prove that “<><>

Exercise 8

Let P = {x ∈ R: x > 0}. Show that P satisfies the following:

(a) If x, y ∈ P, then x + y ∈ P.

(b) If x, y ∈ P, then x ⋅ y ∈ P.

(c) For each x ∈
, exactly one of the following three statements is true: x ∈ P, x = 0, − x ∈ P.