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Chapter 3: Q13-18P (page 179)

Show that division cannot be a group operation. Hint: See (13.7 d).

Short Answer

Expert verified

Division is not a group operation

Step by step solution

01

Given Information

The division operation

02

Group operation

The ordered pair of a set and a binary operation on this set that fulfills the group axioms is referred to as the group. The set is known as the group's underlying set, and the operation is known as the group operation or the group rule.

03

The division is not Group Operation

The division of numbers is not a group because it is not associative.

$(\frac{a}{\frac{b}{c}}) = \frac{a c}{b} (\frac{\frac{a}{b}}{c}) = \frac{a}{h r}$

Which does not give the same result. Hence division is not a group operation.

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