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consider the poset ({2, 4, 5, 10, 20}, |). what are the maximal elements, the minimal elements, the greatest element, and the least element of the poset?

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Maximal elements are 10 and 20, minimal elements are 2 and 4, there is neither greatest element and nor least element.

→ The maximal element in the poset is an element that is divisible by all elements in poset is comparable to. so 10 and 20 are the maximal elements.

→The minimal element in the poset is an element that is divisible by all other elements in the relation they are comparable to. so 2 and 4 are minimal elements.

→There is no greatest element because 10 and 20 are incomparable which means that one doesn't precede the other.

→There is no least element because 2 and 4 are incomparable which means that one doesn't precede the other.

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