The largest and maximal elements

Task number: 4151

In the following cases decide, whether exists a partial oder satisfying the given condition. If so, show an example.

  • Variant

    Without the largest element, but with a maximal element; on a nonempty finite set.

  • Variant

    Without the largest element, and without the smallest element; on a nonempty finite set.

  • Variant

    Without the largest element, and without the maximal element; on a nonempty finite set.

  • Variant

    Without the largest element, but with a maximal element; on an infinite set.

  • Variant

    Without the largest element, and without maximal element; on an infinite set.

  • Variant

    Without infinite chain, on an infinite set.

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