Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c }
\| & 4 & 7 & 12 & 19 \
\hline 4 & 4 & 7 & 12 & 19 \
7 & 7 & 12 & 19 & 4 \
12 & 12 & 19 & 4 & 7 \
19 & 19 & 4 & 7 & 12
\end{array}$$
A) All of them
B) None of them
C) Closure, identity, inverse, 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.
-$$\begin{array} { c | c c c c } 
\| & 4 & 7 & 12 & 19 \
\hline 4 & 4 & 7 & 12 & 19 \
7 & 7 & 12 & 19 & 4 \
12 & 12 & 19 & 4 & 7 \
19 & 19 & 4 & 7 & 12
\end{array}$$
A) All of them
B) None of them
C) Closure, identity, inverse, and commutative only
D) Closure, identity, inverse, and associative only

Quizplus · Accepted Answer

The given system satisfies all the properties of a commutative group: closure (every operation on two elements from the set results in an element from the set), identity (4 acts as the identity element since operating it with any element returns that element), inverse (each element can be operated with another to return the identity element), associative (the operation between any three elements can be grouped in any way and yield the same result), and commutative (the result of the operation does not depend on the order of the elements).

Decide Which of the 5 Properties of a Commutative Group