Comparing finite sets

Task number: 3376

Prove by mathematical induction that for all finite sets \(X\) and \(Y\):

  • Variant

    If there exists an injective mapping from \(X\) to the set \(Y\), then \(|X|\leq |Y|\).

  • Variant

    If there exists a surjective mapping from \(X\) to \(Y\), then \(|X|\geq |Y|\).

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