Register

UGC NET CSE | June 2019 | Part 2 | Question: 1

• edited by
7,708 views
8 votes
8 votes

Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$

Which of the following is correct  for the given poset ?

  1. There exist a greatest element and a least element
  2. There exist a greatest element but not a least element
  3. There exist a least element but not a greatest element
  4. There does not exist a greatest element and a least element
• edited by
User Avatar

3 Answers

Best answer
8 votes
8 votes

There are two maximal elements $24$ and $45$.

There are two minimal elements $5$ and $3$.

So there is no greatest and least element.

$\therefore$ Option $4.$ is correct.

• edited by
User Avatar
3 votes
3 votes

   1-We can not choose here greatest element because two maximal element(24,45 are at same level in Hasse diagram) are there.                                                                                                                                                                                                                              2-We can not choose here least element because two minimal element(3,5 are at same level in Hasse diagram) are there.                                                                                                                                                                                                                                          So: Option 4 is correct.

• edited by
User Avatar
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

5.4k
views
2 answers
1 votes
Arjun asked Jul 2, 2019
5,435 views
UGC NET CSE | June 2019 | Part 2 | Question: 9
Find the zero-one matrix of the transitive closure of the relation given by the matrix $A$ :$$A =\begin{bmatrix} 1 & 0& 1\\ 0 & 1 & 0\\ 1& 1& 0 \end{bmatrix}$$$\begin{bma...
User Avatar
1.9k
views
1 answers
2 votes
Arjun asked Jul 2, 2019
1,859 views
UGC NET CSE | June 2019 | Part 2 | Question: 70
Consider the following statements:$S_1$: For any integer $n>1, \: a^{\phi(n)} \equiv 1(mod \: n)$ for all $a \in Z_n^*$ , where $\phi(n)$ is Euler’s phi function.$S_2$:...
User Avatar
1.3k
views
1 answers
3 votes
Arjun asked Jul 2, 2019
1,341 views
UGC NET CSE | June 2019 | Part 2 | Question: 13
How many different Boolean functions of degree $n$ are the$2^{2^n}$$(2^2)^n$$2^{2^n} -1$$2^n$
User Avatar
1.2k
views
2 answers
0 votes
srestha asked May 18, 2019
1,196 views
Made Easy Test Series:Discrete Mathematics-Poset
Consider the following Posets:$I)\left ( \left \{ 1,2,5,7,10,14,35,70 \right \},\leq \right )$$II)\left ( \left \{ 1,2,3,6,14,21,42 \right \},/ \right )$$III)\left ( \lef...
User Avatar
Link Copied!