On a board with three rows and two columns of squares, a coin is placed on each of the
Chapter 11, Problem 8(choose chapter or problem)
On a board with three rows and two columns of squares, a coin is placed on each of the two lowest squares. This is called position 1 and is denoted by P1 (see Figure 11.33). A legal move on the board consists of moving one of the coins to the next higher square. This results in nine possible positions for the coins on the squares. Let S = {P1, P2, . . . , P9}. Define a relation _ on S by Pi Pj if the coins must be in position Pi before they can be in position Pj . Then (S,_) is a poset. (a) Draw a Hasse diagram of (S,_). (b) Is (S,_) a lattice?
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