Let's analyze each statement one by one to determine if it's true or false:
1. Zero is greater than all negative integers:
- Zero is a neutral number. By definition, it is greater than any negative integer.
- Conclusion: This statement is true.
2. -15 is greater than -6:
- On the number line, -15 is further to the left than -6, which means -15 is less than -6.
- Conclusion: This statement is false.
3. The sum of a positive integer and a negative integer is always a positive integer:
- The result of adding a positive integer and a negative integer depends on their magnitudes. It could be positive, negative, or zero. For example, [tex]\(5 + (-3) = 2\)[/tex] (positive) and [tex]\(3 + (-5) = -2\)[/tex] (negative).
- Conclusion: This statement is false.
4. Additive inverse of -17 is 17:
- The additive inverse of a number is the number that, when added to the original number, results in zero. For -17, the additive inverse is indeed 17 because [tex]\(-17 + 17 = 0\)[/tex].
- Conclusion: This statement is true.
5. Associative property holds for addition and subtraction of integers:
- The associative property states that for addition, the grouping of numbers does not affect the sum, i.e., [tex]\((a + b) + c = a + (b + c)\)[/tex].
- For subtraction, however, the grouping does matter, i.e., [tex]\((a - b) - c \neq a - (b - c)\)[/tex] in general.
- Conclusion:
- For addition: true.
- For subtraction: false.
So, the evaluations of the statements are as follows:
1. True
2. False
3. False
4. True
5. Addition: True, Subtraction: False
