1 Attachment(s)

supremum and infimum of a set

M={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A={3, 4, 5}, B={9, 12}, C={1, 4, 8}.

The graph is attached.

I need to find the supremum, infimum, max, min of the sets, the biggest and the smallest element.

I have the following answer in the book.

М - hasn't got a smallest and biggest element

min elements are 11 и 12.

max elements are 6, 7, 9 и 10.

А*={7}, supA=7, A*={1, 11}, infA=1

B*=∅, supB hasn't got , B*=∅, infB hasn't got

C*={8, 10}, supC=8, C*={1, 11}, infC=1.

I have no idea how they got he answers. I hope you can help me with this one.