Determine which properties the given mathematical system exhibits. Identify any systems that are groups or Abelian groups.
$\begin{array}{c|ccc}
\Omega & 7 & 9 & 3 \
\hline 7 & 9 & 3 & 7 \
9 & 3 & 7 & 9 \
3 & 7 & 9 & 3
\end{array}$

A) closure, commutative, identity
B) closure, commutative, identity, inverse, associative; Abelian group
C) closure, commutative
D) closure, commutative, identity, inverse

Question

Determine which properties the given mathematical system exhibits. Identify any systems that are groups or Abelian groups.
$\begin{array}{c|ccc}
\Omega & 7 & 9 & 3 \
\hline 7 & 9 & 3 & 7 \
9 & 3 & 7 & 9 \
3 & 7 & 9 & 3
\end{array}$

A) closure, commutative, identity
B) closure, commutative, identity, inverse, associative; Abelian group
C) closure, commutative
D) closure, commutative, identity, inverse

Quizplus · Accepted Answer

The system exhibits closure, commutativity, identity, inverse, and associativity. It is an Abelian group because the operation is commutative.

Determine Which Properties the Given Mathematical System Exhibits Ω793793793793793\begin{array}{c|ccc}\Omega & 7 & 9 & 3 \\\hline 7 & 9 & 3 & 7 \\9 & 3 & 7 & 9 \\3 & 7 & 9 & 3\end{array}Ω793​7937​9379​3793​​

Determine Which Properties the Given Mathematical System Exhibits $\begin{array}{c|ccc}\Omega & 7 & 9 & 3 \\\hline 7 & 9 & 3 & 7 \\9 & 3 & 7 & 9 \\3 & 7 & 9 & 3\end{array}$