Final answer:
An example of a non-commutative binary operation on the set of integers Z is subtraction. As subtraction does not satisfy the commutative property where changing the order of the operands does not change the result, it serves as an appropriate example with results such as 5 - 3 not being equal to 3 - 5.
Step-by-step explanation:
An example of a non-commutative binary operation on the set of integers Z is subtraction. In mathematics, a binary operation is said to be commutative if changing the order of the operands does not change the result. However, subtraction does not satisfy this property.
For example, consider the integers 5 and 3. The expression 5 - 3 equals 2, whereas 3 - 5 equals -2. Since 2 is not equal to -2, we can conclude that subtraction is not commutative.
To further illustrate this concept, let's take two arbitrary integers from the set Z, say a and b. If we subtract b from a, we get a - b. If we reverse the order and subtract a from b, we get b - a. These two results are only the same if a and b are equal; otherwise, the results are different, proving that subtraction is a non-commutative operation on Z.