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 
and an operation 
meaning
"followed by." Thus, 
means "left face" followed by "left face" and is the same as the single command "about face." Complete the following table.
a l r f a 0 l a r 0 f ?
A. a l r f
a f r l a
l r f f l
r l f a r
f a l r f
?
B.
a l r fa r l a f
l l f l a
r a l r a
f f r a f
?
C.
a l r fa f r l a
l r a f l
r l f a r
f a l r f
?
D.
a l r fa r a f l
l a f a r
r f a r f
f l r f a
?
Answer: C
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> 0
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A. 
B. 
C. 
D. 