Question

For each of the following statements write (T) for true and (F) for false:
(i) The sum of two negative integers is always a negative integer.
(ii) The sum of a negative integer and a positive integer is always a negative integer.
(iii) The sum of an integer and its negative is zero.
(iv) The sum of three different integers can never be zero.
(v) | −5| < |−3|
(vi) |8 − 5| = |8| + |−5|

Answer 1

(i) True
For example: - 2 + (-1) = -3

(ii) False
It can be negative or positive.
For example: -2 + 3 = 1 gives a positive integer, but -5 + 2 = -3 gives a negative integer.

(iii) True
For example: 100 + (-100) = 0

(iv) False
For example: (-5) + 2 + 3 = 0

(v) False
|-5| = 5 and | -3 | = 3, 5 > 3

(vi) False
|8 − 5| = 3
|8| + |−5| = 8 + 5
= 13
$\therefore$ |8 − 5|$\ne$|8| + |−5|