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Math / Linear Algebra 4 / Chapter 1.7 / Problem 1

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

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Label the following statements as true or false. (a) Every family of sets contains a

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QUESTION:

Label the following statements as true or false. (a) Every family of sets contains a maximal element. (b) Every chain contains a maximal element. (c) If a family of sets has a maximal element, then that maximal element is unique. (d) If a chain of sets has a maximal clement, then that maximal element is unique. (e) A basis for a vector space is a maximal linearly independent subset of that vector space. (f) A maximal linearly independent subset of a vector space is a basis for that vector space.

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QUESTION:

Label the following statements as true or false. (a) Every family of sets contains a maximal element. (b) Every chain contains a maximal element. (c) If a family of sets has a maximal element, then that maximal element is unique. (d) If a chain of sets has a maximal clement, then that maximal element is unique. (e) A basis for a vector space is a maximal linearly independent subset of that vector space. (f) A maximal linearly independent subset of a vector space is a basis for that vector space.

ANSWER:

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Let be a family of sets. A member of is called maximal if is contained in no members of other than itself.

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