Which of the following is true of the commutative property under subtraction? a) (A - B ≠ B - A)  b) (A - B = B - A)

We will use the concept of the commutative property of subtraction to find out which is true.

Answer : (A - B ≠ B - A) is true and (A - B = B - A) is false

Let's see how we will use the concept of the commutative property of subtraction to find out which is true.

Explanation :

Given to us is two expressions 

1) A - B ≠ B - A

2) A - B = B - A

The commutative property says that if (A operator B ) gives us some result then ( B operator A ) should also give us the same result.

But for the above two expressions, we know by the knowledge of subtraction that A - B can never be equal to B - A unless both A and B are equal to 0.

We can observe this by taking a simple example, where A = 4 and B = 6 

Therefore A - B = 4 - 6 = -2

and B - A = 6 - 4 = 2

Hence, we clearly observe that A - B ≠ B - A.

So expression 1 is true i.e. A - B ≠ B - A.

Hence  (A - B ≠ B - A) is true and (A - B = B - A) is false.