Is the set H from Problem 56 closed for the operation of ? Data from problem 56

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Is the set H from Problem 56 closed for the operation of image?

Data from problem 56

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

"left face" by l, "right face" by r, "about face" by a, and "stand fast" by f. (The element f means "don't

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