Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c }
? & \vee & ¥ & \Theta \
\hline \vee & \vee & \Theta & ¥ \
¥ & \Theta & ¥ & \vee \
\Theta & ¥ &£ & \vee
\end{array}$$
A) None of them
B) Closure only
C) Closure, identity, associative, and commutative only
D) Closure, identity, inverse, and associative only

Question

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c } 
? & \vee & ¥ & \Theta \
\hline \vee & \vee & \Theta & ¥ \
¥ & \Theta & ¥  & \vee \
\Theta & ¥  &£  & \vee   
\end{array}$$
A) None of them
B) Closure only
C) Closure, identity, associative, and commutative only
D) Closure, identity, inverse, and associative only

Quizplus · Accepted Answer

The given operation table does not satisfy any of the properties of a commutative group. There is no clear identity element, inverses are not evident, associativity is not guaranteed, and the operation is not commutative.

Decide Which of the 5 Properties of a Commutative Group