Exercise 1.2.5 Show that for 1 ≤ p ≤ ∞, ||x|| is a norm in the space Rd. The main task is to veryy the triangle inequality, which can be done by first proving the Hölder inequality, x·y| ≤ ||x||p||y||p', x, y e Rd. Here p' is the conjugate of p defined through the relation 1/p' + 1/p = 1; by convention, p' = 1 if p = ∞, p' = ∞ if p = 1.

Q: Illustrate the following (A ∩ B') = A' U B'

A: To illustrate the set equality (A ∩ B') = A' U B', we'll use Venn diagrams. Venn diagrams are…

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Q: IV. Find two positive numbers such that their sum is 20 and their product is as large as possible.

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Q: A ∩ B' = (A' ∪ B)' True or False

A: Demorgan theorem: