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

Solution:

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

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

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.

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

Summary:

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