. For each of these intervals, list all its elements or explain why it is empty. a) [a, a] b) [a, a) c) (a, a] d) (a, a) e) (a,

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natulia

11 days ago

5

. For each of these intervals, list all its elements or explain why it is empty. a) [a, a] b) [a, a) c) (a, a] d) (a, a) e) (a,

b), where a > b f ) [a, b], where

Mathematics

1 answer:

tester [11.8K] · Answer 1 · 2026-03-29T05:39:49+03:00

The elements can be listed in the following format: (i) [a,a], (ii) [a,a), (iii) (a,a], (iv) (a,a), (v) (a,b) with a > b, and (vi) [a,b] with a > b. Let's explain them: (i) [a,a] suggests that only the point a is included. Since it is a single point, this set is empty. (ii) [a,a) means it includes a but excludes the right side. It is also empty since it can't include any other values. (iii) (a,a] includes values up to a but not a itself, which leaves it empty too. (iv) (a,a) completely excludes a on both sides, so this set is empty. (v) (a,b) where a > b means it has no values since a can't be greater than b in an interval. (vi) [a,b] includes both a and b, but since a > b is stated, this interval leads to an empty set.