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 ∈ ℝ, exactly one of the following three statements is true:
x ∈ P, x = 0, − x ∈ P.
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