Identify whether the following collections of subsets are partitions of R, the set of real numbers, and the correct reason for it: the set of intervals [k, k+1], k = ..., −2, −1, 0, 1, 2, ... Multiple Choice The given collection of sets does not form a partition of R as these sets are not pairwise disjoint. О The given collection of sets forms a partition of R as these sets are not pairwise disjoint and their union is not R. О The given collection of sets does not form a partition of R as the union of these sets is not R. о The given collection of sets forms a partition of R as these sets are pairwise disjoint and their union is R. Identify whether the following collections of subsets are partitions of R, the set of real numbers, and the correct reason for it: the set of irrational numbers, the set of rational numbers Multiple Choice О The given collection of sets forms a partition of R as these sets are not pairwise disjoint and their union is not R. The given collection of sets forms a partition of R as these sets are pairwise disjoint and their union is R. The given collection of sets does not form a partition of R as these sets are not pairwise disjoint. The given collection of sets does not form a partition of R as the union of these sets is not R.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.1: Basic Assumptions
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Identify whether the following collections of subsets are partitions of R, the set of real numbers, and the correct reason for
it:
the set of intervals [k, k+1], k = ..., −2, −1, 0, 1, 2, ...
Multiple Choice
The given collection of sets does not form a partition of R as these sets are not pairwise disjoint.
О
The given collection of sets forms a partition of R as these sets are not pairwise disjoint and their union is not R.
О
The given collection of sets does not form a partition of R as the union of these sets is not R.
о
The given collection of sets forms a partition of R as these sets are pairwise disjoint and their union is R.
Transcribed Image Text:Identify whether the following collections of subsets are partitions of R, the set of real numbers, and the correct reason for it: the set of intervals [k, k+1], k = ..., −2, −1, 0, 1, 2, ... Multiple Choice The given collection of sets does not form a partition of R as these sets are not pairwise disjoint. О The given collection of sets forms a partition of R as these sets are not pairwise disjoint and their union is not R. О The given collection of sets does not form a partition of R as the union of these sets is not R. о The given collection of sets forms a partition of R as these sets are pairwise disjoint and their union is R.
Identify whether the following collections of subsets are partitions of R, the set of real numbers, and the correct reason for
it:
the set of irrational numbers, the set of rational numbers
Multiple Choice
О
The given collection of sets forms a partition of R as these sets are not pairwise disjoint and their union is not R.
The given collection of sets forms a partition of R as these sets are pairwise disjoint and their union is R.
The given collection of sets does not form a partition of R as these sets are not pairwise disjoint.
The given collection of sets does not form a partition of R as the union of these sets is not R.
Transcribed Image Text:Identify whether the following collections of subsets are partitions of R, the set of real numbers, and the correct reason for it: the set of irrational numbers, the set of rational numbers Multiple Choice О The given collection of sets forms a partition of R as these sets are not pairwise disjoint and their union is not R. The given collection of sets forms a partition of R as these sets are pairwise disjoint and their union is R. The given collection of sets does not form a partition of R as these sets are not pairwise disjoint. The given collection of sets does not form a partition of R as the union of these sets is not R.
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