Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c }
?? & 2 & 8 & 11 & 16 \
\hline 2 & 8 & 11 & 16 & 2 \
8 & 11 & 16 & 2 & 8 \
11 & 16 & 2 & 8 & 11 \
16 & 2 & 16 & 11 & 8
\end{array}$$
A) Closure, identity, and inverse only
B) Closure only
C) Closure, identity, inverse, and commutative only
D) All of them

Question

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c } 
?? & 2 & 8 & 11 & 16 \ 
\hline 2 & 8 & 11 & 16 & 2 \
8 & 11 & 16 & 2 & 8 \
11 & 16 & 2 & 8 & 11 \
16 & 2 & 16 & 11 & 8
\end{array}$$
A) Closure, identity, and inverse only
B) Closure only
C) Closure, identity, inverse, and commutative only
D) All of them

Quizplus · Accepted Answer

The operation is closed as all results are within the set {2, 8, 11, 16}. There is no identity element since no element leaves others unchanged, and no inverses since no element can combine with another to yield an identity. The operation is not associative or commutative based on the table.

Decide Which of the 5 Properties of a Commutative Group