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Independence and inclusion

Task number: 2522

Let V be a vector space and XYV. Decide, which of the following claims are valid or not:

  • Variant 1

    The se X is not independent, while the set Y is independent.

  • Variant 2

    If the set X is independent, so is the set Y.

  • Variant 3

    If the set Y is independent, o is the set X.

Difficulty level: Easy task (using definitions and simple reasoning)
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