the following distance function is a metric on X. Let x = = (x₁, x₂), y = (91, 92) and z = (21, 22) (i).d(x, y) = √√√√(x₁ − y₁)² + (x2 − y2)² (Hint: Use the Minkowski's Inequality: √(an+bn)² ≤√√Σan² + √b² where an, bn are real numbers. x₁ - y₁| + x2 - y₂| (ii). d(x, y) = (iii). d(x, y) = max {|x1 - y₁|, |x2 - y2|}. 3. Extend each of the above three distance functions to define on X = R" and show that in each case the distance function is a metric.

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A:

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A:

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A:

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