Independence and inclusion

Task number: 2522

Let \(V\) be a vector space and \(X\subseteq Y \subseteq V\). 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)
Proving or derivation task
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