Consider a soldier facing in a given direction (say, north). Let us denote left face by ,

Consider a soldier facing in a given direction (say, north).
Let us denote

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"left face" by , "right face" by r, "about face" by a, and "stand fast" by f. (The element f means "don't move from your present position." It does not mean "return to your original position.") Then we define H = {1, r, a, f} and an operation meaning "followed by." Thus, = a means "left face" followed by "left face" and is the same as the single command "about face." Complete the following table. l r a f l a r a a r l f ( r