(Solved): 41. (You need not ETEXthis problem - you can neatly hand-write your answers) See the poset diagram ...

41. (You need not ETEXthis problem - you can neatly hand-write your answers) See the poset diagram below: Ihis is a rather weird partial ordering of the integers 1-9 that IIl call the Star Wars ordering. For example, we have $8?9,9?1,6?5$, etc and specifically $m?n$ iff Episode $n$ of Star Wars is a beteer movié(than Episode m. Note that for example, 7,1 , and 2 are incomprible (equally mediocre), but they are all better than 9. 7, 1, and 2 are all inftrior to 3 which in turn in infariot to both 4 and 6 . a For euch $n=1,2,\dots 9$, show how to compate $A(s,n)$. b. For esch $n$ A B. show how to compute $?(9,n)$