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.