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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.1, Problem 85E

**(a)**

To determine

Whether: subtraction is commutative.

Expert Solution

Subtraction is not commutative.

**Calculation:**

**Try **to find a counterexample to the statement “Subtraction is commutative.” If we can find even example in which subtraction is not commutative, we can say that the statement is false. Let’s assume that subtraction is commutative. This means that for any numbers

Let’s take two numbers. Let

Let’s perform the subtractions.

Now, reverse the numbers,

Since 1 and -1 are not equal, the subtraction order cannot be switched to produce the same results. This provides a counterexample for our argument. Therefore, subtraction is not commutative.

**(b)**

To determine

Whether the division of nonzero real numbers commutative.

Expert Solution

For nonzero real numbers division is not commutative.

**Calculation:**

Try to find a counterexample to the statement “divison is commutative.” If we can find even example in which subtraction is not commutative, we can say that the statement is false.

Let’s assume that division is commutative. This means that for any nonzero numbers

Let’s take two nonzero real numbers. Let

Let’s perform the divisions.

Now, reverse the numbers,

Since 2 and