Write 'T' for true and 'F' for false in each of the following :
(i) 0 is neither positive nor negative.
(ii) `-(-36) - 1 = - 37`.
(iii) On the number line `-10` lies to the right of `-6`.
(iv) 0 is an integer.
(v) `-| - 15| = - 15`.
(vi) `|-40| + 40 = 0 `.

Answer

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

### Step-by-Step Solution:

**(i)** **Statement:** 0 is neither positive nor negative.
**Solution:**
- The number 0 is considered neutral. It does not fall into the category of positive or negative numbers.
**Answer:** T (True)

**(ii)** **Statement:** `-(-36) - 1 = -37`.
**Solution:**
- First, simplify `-(-36)`, which equals 36 (since the negative of a negative number is positive).
- Now, calculate: `36 - 1 = 35`.
- The statement claims it equals -37, which is incorrect.
**Answer:** F (False)

**(iii)** **Statement:** On the number line `-10` lies to the right of `-6`.
**Solution:**
- On a number line, numbers decrease as you move left.
- `-10` is to the left of `-6`, not the right.
**Answer:** F (False)

**(iv)** **Statement:** 0 is an integer.
**Solution:**
- Integers include all whole numbers, both positive and negative, as well as zero.
- Therefore, 0 is indeed an integer.
**Answer:** T (True)

**(v)** **Statement:** `-| - 15| = - 15`.
**Solution:**
- The absolute value of `-15` is `15`, so `| - 15| = 15`.
- Therefore, `- | - 15| = -15`.
- This statement is correct.
**Answer:** T (True)

**(vi)** **Statement:** `|-40| + 40 = 0`.
**Solution:**
- The absolute value of `-40` is `40`, so `|-40| = 40`.
- Therefore, `40 + 40 = 80`, not 0.
**Answer:** F (False)

### Final Answers:
1. (i) T
2. (ii) F
3. (iii) F
4. (iv) T
5. (v) T
6. (vi) F