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| lt |-3|`
(vi) `|8 -5| = |8| + |-5|`

Answer

Let's analyze each statement one by one and determine whether they are true (T) or false (F).

### Step-by-Step Solution:

**(i)** The sum of two negative integers is always a negative integer.
- **Explanation:** When you add two negative integers, the result is always negative. For example, -5 + (-3) = -8, which is negative.
- **Conclusion:** This statement is **True (T)**.

**(ii)** The sum of a negative integer and a positive integer is always a negative integer.
- **Explanation:** This is not always true. For example, if we take -2 (negative integer) and +3 (positive integer), their sum is -2 + 3 = 1, which is positive.
- **Conclusion:** This statement is **False (F)**.

**(iii)** The sum of an integer and its negative is zero.
- **Explanation:** This statement is true. For any integer 'a', the sum of 'a' and its negative (-a) is always zero. For example, 7 + (-7) = 0.
- **Conclusion:** This statement is **True (T)**.

**(iv)** The sum of three different integers can never be zero.
- **Explanation:** This statement is false. For example, if we take the integers -2, 3, and -1, their sum is -2 + 3 + (-1) = 0.
- **Conclusion:** This statement is **False (F)**.

**(v)** `|-5| < |-3|`
- **Explanation:** The absolute value of -5 is 5, and the absolute value of -3 is 3. So, 5 is not less than 3.
- **Conclusion:** This statement is **False (F)**.

**(vi)** `|8 - 5| = |8| + |-5|`
- **Explanation:** The left side calculates to |3| = 3. The right side calculates to |8| + |-5| = 8 + 5 = 13. Since 3 is not equal to 13, this statement is false.
- **Conclusion:** This statement is **False (F)**.

### Final Answers:
- (i) T
- (ii) F
- (iii) T
- (iv) F
- (v) F
- (vi) F