
(a)
To find: the order of element 3 in the group
(a)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of an additive group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(b)
To find: the order of element 3 in the group
(b)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of an additive group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(c)
To find: the order of element 3 in the group
(c)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of an additive group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(d)
To find: the order of element 3 in the group
(d)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of an additive group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(e)
To find: the order of element 3 in the group
(e)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of an additive group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(f)
To find: the order of element 3 in the group
(f)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of a multiplicative group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(g)
To find: the order of element 3 in the group
(g)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of a multiplicative group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
(h)
To find: the order of element 3 in the group
(h)

Answer to Problem 8E
The order of the element 3 of the group
Explanation of Solution
Concept used:
The order of an element ‘a’ of a multiplicative group is defined as the least positive integer n such that
Calculation:
Consider the group
Now, for the element 3 of the group
Thus, the order of the element 3 of the group
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Chapter 6 Solutions
A Transition to Advanced Mathematics
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