Final answer:
The statement a - b = b - a is not always true. The order of subtraction matters when subtracting sets. Here's an example to illustrate this.
Step-by-step explanation:
The statement a - b = b - a is not always true. In fact, it is usually false. When we subtract set b from set a, we're essentially removing any elements that are common to both sets. On the other hand, when we subtract set a from set b, we're removing any elements that are common to both sets. These operations are not commutative, which means the order of subtraction matters.
For example, let's consider the sets a = {1, 2, 3} and b = {2, 3, 4}. When we calculate a - b, we remove the elements that are common to both sets, so the result is a = {1}. On the other hand, when we calculate b - a, we get b = {4}.
Thus, we can see that a - b is not equal to b - a in this case. Therefore, we have disproven the statement.