2. For each of the following, X represents Rx R. Prove that each of the following distance function is a metric on X. Let x = (₁, ₂), y (91, 92) and z = (21, 22) (i).d(x, y) = √(x1 - y₁)² + (x2 - y₂)² (Hint: Use the Minkowski's Inequality: √Σ(an + bn)² ≤ √Σan² + √b² where an, bn are real numbers. (ii). d(x, y) = x₁y₁| + x2 - y2| (iii). d(x, y): = max {x₁y₁, x2 - y2|}.

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