Consider the four basic military commands: Attention!LeftFace!(E)(L)RightFace!AboutFace!(R)(A)
Let G={E,L,R,A}= the set of four basic military commands and define the operation in the following
manner: If a,bG, then ab=c means "starting at position a after a has been performed from the
original position, the original position being a, execute command b and the result c is the final
position based on the original position." For instance, L * A means we start facing left and then do
"About Face!". This will give us R. Another, if we have AR, we start facing backward and then turn
right. The result will be L. Now, do the activity below: Activity 1 1. Suppose we call the results of
the operation * as sums. Compute all the sums of E, L, R and A in the following table. 2.
Considering the table, compute a. L(RA) b. (LR)A Are they equal? How many such tests would be
necessary to prove that this system is associative? 3. Is there any identity element? Which one? 4.
Find the inverse of E, of L, of R, and of A. 5. Is (G,) a group? Justify. 6. Is it abelian? 7. What are
the subgroups of G ?.
Consider the four basic military commands AttentionLeft.pdf
1. Consider the four basic military commands: Attention!LeftFace!(E)(L)RightFace!AboutFace!(R)(A)
Let G={E,L,R,A}= the set of four basic military commands and define the operation in the following
manner: If a,bG, then ab=c means "starting at position a after a has been performed from the
original position, the original position being a, execute command b and the result c is the final
position based on the original position." For instance, L * A means we start facing left and then do
"About Face!". This will give us R. Another, if we have AR, we start facing backward and then turn
right. The result will be L. Now, do the activity below: Activity 1 1. Suppose we call the results of
the operation * as sums. Compute all the sums of E, L, R and A in the following table. 2.
Considering the table, compute a. L(RA) b. (LR)A Are they equal? How many such tests would be
necessary to prove that this system is associative? 3. Is there any identity element? Which one? 4.
Find the inverse of E, of L, of R, and of A. 5. Is (G,) a group? Justify. 6. Is it abelian? 7. What are
the subgroups of G ?
