SOLUTION: Given: The following table represents the operation # on the set G = {a, b, c, d} # a b c d a a b c d b b c d a c c d a b d d a b c A. Explain why the set G is close

Algebra ->  Sequences-and-series -> SOLUTION: Given: The following table represents the operation # on the set G = {a, b, c, d} # a b c d a a b c d b b c d a c c d a b d d a b c A. Explain why the set G is close      Log On


   

Question 1074887: Given:

The following table represents the operation # on the set G = {a, b, c, d}
# a b c d
a a b c d
b b c d a
c c d a b
d d a b c
A. Explain why the set G is closed under the operation #.

B. Explain why a is the identity element for #.

C. Verify two cases of the commutative property.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A. The output of the operation is contained in G.
.
.
.
B. Because
a#a=a#a=a
a#b=b#a=b
a#c=c#a=c
a#d=d#a=d
.
.
.
C. b#c=d
c#b=d
So b#c=c#b.
.
.
.
You can do the other case.
Just look for any other combination but don't use a in the operation since it's the identity element.