UGC NET Computer Science June 2019 -II | Question 1 (Shift-I)

Question 1

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1. Consider the poset ({3,5,9,15,24,45},|).
Which of the following is correct for the given poset?

1. (1) There exists a greatest element and a least element
2. (2) There exists a greatest element but not a least element
3. (3) There exists a least element but not a greatest element
4. (4) There does not exist a greatest element and a least element

Answer : (4) There does not exist a greatest element and a least element

Explanation Question 1

The division symbol ‘|’ is a partial ordering on the set {3,5,9,15,24,45}.
Lets draw Hasse Diagram for the given partially ordered set, or poset.

Hasse Diagram for given poset ({3,5,9,15,24,45},|)

For given poset, We can not choose greatest element because there are two maximal elements 24 and 45.

Similarly, We can not choose here least element because there are two minimal elements 5 and 3 at same level in Hasse diagram.

So, there is no possibility of greatest and least element.

So, option (4) is correct answer

Reference : Partial Orderings - partially ordered set / poset

Reference : Greatest element of a subset S of a partially ordered set (poset)

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