Chapter 5.1, Problem 56PS

Problem Solving Level 3

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 move from your present position.” It does not mean “return to your original position.”) Then we define

$H=\left\{l,r,a,f\right\}$

And an operation ⋆ meaning “followed by.” Thus, $l$⋆ $l=a$ means “left face” followed by “left face” and is the same as the single command “about face.” Complete the following table.

⋆	$l$	$r$	$a$	$f$
$l$	$a$
$r$
$a$
$f$