Let's analyze each option to determine which ones are true statements regarding the commutative property under subtraction.
Option A: [tex]\(10 - 9 \neq 9 - 10\)[/tex]
- Subtraction is not commutative, meaning changing the order of the numbers does change the result.
- Calculating each side:
- [tex]\(10 - 9 = 1\)[/tex]
- [tex]\(9 - 10 = -1\)[/tex]
- Since [tex]\(1 \neq -1\)[/tex], this statement is true.
Option B: [tex]\(10 - 9 = 10 - 9\)[/tex]
- This is comparing the subtraction of the same values in the same order.
- Clearly,
- [tex]\(10 - 9 = 1\)[/tex]
- [tex]\(10 - 9 = 1\)[/tex]
- Therefore, [tex]\(1 = 1\)[/tex], making this statement true.
Option C: [tex]\(10 - 9 = 10 + 9\)[/tex]
- This option is comparing subtraction to addition.
- Calculating each side:
- [tex]\(10 - 9 = 1\)[/tex]
- [tex]\(10 + 9 = 19\)[/tex]
- Since [tex]\(1 \neq 19\)[/tex], this statement is false.
Option D: [tex]\(10 + 9 = 9 + 10\)[/tex]
- This option is utilizing the commutative property of addition, which is commutative.
- Calculating each side:
- [tex]\(10 + 9 = 19\)[/tex]
- [tex]\(9 + 10 = 19\)[/tex]
- Since [tex]\(19 = 19\)[/tex], this statement is true.
Based on the analysis above, the true statements regarding subtraction and the commutative property are:
- Option A: [tex]\(10 - 9 \neq 9 - 10\)[/tex]
- Option B: [tex]\(10 - 9 = 10 - 9\)[/tex]
- Option D: [tex]\(10 + 9 = 9 + 10\)[/tex]
The answer can be summarized as:
[tex]\[
\boxed{1, 1, 0, 1}
\][/tex]
