the last two are kind of giving me problems so if anyone has any ideas, I'd really appreciate it. 4. Let d₁ and d2 be metrics on sets X and Y respectively. Prove that(i) d is a metric on X x Y, whered((x1, y₁), (x2, y2)) = max{d₁(x1, x2), d2(y₁, y2)}.(ii) e is a metric on X x Y, wheree((x1, y₁), (x2, y2)) = d₁(x₁, x2)+d2(y1, y2).(iii) d and e are equivalent metrics.

To show that e is metric on X×Y we have to prove three property a) non-negativity b) symmetry c)…

Answered: 4. Let d₁ and d2 be metrics on sets X…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Let d₁ and d2 be metrics on sets X and Y respectively. Prove that (i) d is a metric on X x Y, where d((x1, y1), (x2, y2)) = max{d₁(x1, x2), d2(y1, y2)}. (ii) e is a metric on X x Y, where e((x1, y₁), (x2, y2)) = d₁(x1, x2)+d2(y1, 32). (iii) d and e are equivalent metrics.