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Let A be a nonempty subset of R that is both bounded above and below and let B be a nonempty subset of A. Prove or disprove each of the following assertions. (a) inf(A) ≤ inf(B) ≤ sup(B) ≤ sup(A). (b) If inf(A) = sup(A), then A has exactly one element. (c) If inf(A) = inf(B) and sup(A) = sup(B), then A = B.

Let A be a nonempty subset of R that is both bounded above and below and let B be a nonempty subset of A. Prove or disprove each of the following assertions. (a) inf(A) ≤ inf(B) ≤ sup(B) ≤ sup(A). (b) If inf(A) = sup(A), then A has exactly one element. (c) If inf(A) = inf(B) and sup(A) = sup(B), then A = B.

Advanced Engineering Mathematics
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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Let A be a nonempty subset of R that is both bounded above and
below and let B be a nonempty subset of A. Prove or disprove each
of the following assertions.
(a) inf(A) ≤ inf(B) ≤ sup(B) ≤ sup(A).
(b) If inf(A) = sup(A), then A has exactly one element.
(c) If inf(A) = inf(B) and sup(A) = sup(B), then A = B.

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