A positive integer minus a positive integer is always positive.

This statement is sometimes true. For example, 17 – 5 = 12, but 15 – 20 = –5.

post five other statements about the addition and subtraction of positive and negative integers, and ask whether each is always true, sometimes true, or never true.

If only two numbers are involved,

Let A and B be real, non-zero numbers.

1) (+)A + (+)B = (+) ?
This is always true.

2) (-)A + (-)B = (-) ?
This is always true.

3) (+)A - (-)B = (+) ?
This is always true.

4) (-)A - (+)B = (-) ?
This is always true.

5) (-)A - (-)B = (+) ?
This is not always true. For instance,
-5 - (-3) = -2, but -3 - (-5) = +2.

Hope this helps~ :3

Statement 1: Adding a positive integer to a positive integer is always positive.

This statement is always true. For example, 6 + 4 = 10, and 23 + 9 = 32.

Statement 2: Adding a positive integer to a negative integer is always negative.
This statement is sometimes true. For example, 6 + (-4) = 2 is positive, but (-3) + (-7) = (-10) is negative.

Statement 3: Subtracting a positive integer from a positive integer is always positive.
This statement is sometimes true. For example, 8 - 3 = 5 is positive, but 5 - 10 = (-5) is negative.

Statement 4: Subtracting a positive integer from a negative integer is always negative.
This statement is always true. For example, (-4) - 3 = (-7), and (-10) - 7 = (-17) are both negative.

Statement 5: Adding a negative integer to a negative integer is always negative.
This statement is always true. For example, (-5) + (-3) = (-8), and (-12) + (-6) = (-18) are both negative.

To determine whether each statement is always true, sometimes true, or never true, we can examine different combinations of positive and negative integers.