Help me answer number 5 only. (3) Prove the Generalized Triangle Inequality: if a₁, a2, ..., an € R then [a₁ + a2 + ··· + ªn| ≤ |a₁| + |a₂| + · · · + |an|.(Hint: Use the Principle of Mathematical Induction)(4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf B ≤ inf Aand (b) sup A ≤ sup B.(5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x is an interiorpoint of A, (b) x is a boundary point of A or (c) x is an exterior point of A.

5. To prove: If x is any real number and any subset A of ℝ, then either x is an interior point of A…

Answered: (5) Show that for any real number x and…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 21E: 21. A relation on a nonempty set is called irreflexive if for all. Which of the relations in...

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(5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x is an interior point of A, (b) x is a boundary point of A or (c) x is an exterior point of A.