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Chapter 5: Problem 96

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Subtraction is a commutative operation.

Short Answer

Expert verified
The statement 'Subtraction is a commutative operation' is false. The correct statement is 'Subtraction is not a commutative operation.'

Step by step solution

01

Understanding Commutativity

A binary operation is said to be commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it.
02

Applying Commutativity to Subtraction

In subtraction, if you swap the order of the operands, the result changes. For instance, the operation \(5-3\) gives the result \(2\), but reversing the operands as in \(3-5\) yields \(-2\). Hence, subtraction is not a commutative operation.
03

Correcting the Statement

To make the statement true, we can correct it as follows: 'Subtraction is not a commutative operation.'

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Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=5000, r=1\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{20}\), when \(a_{1}=2, r=3\).

The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(4,10,16,22, \ldots\)
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