Question #117138
For the poset ({2,4,6,9,12,18,27,36,48,60,72},|) having the `divides’ relation, find
(a) the maximal elements
(b) the minimal elements
(c) All upper bounds of {2,9}
(d) The least upper bound of {2,9} if it exists.
1
Expert's answer
2020-06-08T19:41:10-0400

Let the given set be S={2,4,6,9,12,18,27,36,48,60,72}S=\{2,4,6,9,12,18,27,36,48,60,72\}

1) We known that ,An element mSm\in S is called the maximal element of SS if mx    m=xm | x \implies m=x Where xSx\in S .

Thus 27,48,6027,48,60 and 7070 are the maximal element.

2) We known that ,an element aSa\in S is called the minimal element of SS if xa    x=ax|a\implies x=a Where xSx\in S .

Thus , 2,92,9 are maximal element.

3)The upper bound of {2,9}\{ 2,9\} are 18,36,72

4) Since 18 is the least element of {18,36,72}\{ 18,36,72\} .

Thus , least upper bound of {2,9}\{2,9\} is 18.



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