Write 'T' for true and 'F' for false each of the following :
(i)`(-15)/(-11)`lies to the left of 0 on the number line .
(ii) `(1)/(3)` and `(-3)/(2)` lie on opposite sides of 0 on the number line .
(iii) `(-18)/(13)` lies to the left of 0 on the number line .

Answer

To determine whether each statement is true (T) or false (F), we will analyze each one step by step.

### Step 1: Evaluate the first statement
**Statement (i): `(-15)/(-11)` lies to the left of 0 on the number line.**

1. **Calculate `(-15)/(-11)`:**
- When we divide two negative numbers, the result is positive.
- Therefore, `(-15)/(-11) = 15/11`, which is a positive number.

2. **Determine its position on the number line:**
- Positive numbers lie to the right of 0 on the number line.

**Conclusion for Statement (i):** Since `15/11` is positive, it does not lie to the left of 0. Thus, the statement is **False (F)**.

### Step 2: Evaluate the second statement
**Statement (ii): `(1)/(3)` and `(-3)/(2)` lie on opposite sides of 0 on the number line.**

1. **Identify the values:**
- `1/3` is a positive number (approximately 0.33).
- `-3/2` is a negative number (approximately -1.5).

2. **Determine their positions on the number line:**
- `1/3` lies to the right of 0.
- `-3/2` lies to the left of 0.

**Conclusion for Statement (ii):** Since one number is positive and the other is negative, they lie on opposite sides of 0. Thus, the statement is **True (T)**.

### Step 3: Evaluate the third statement
**Statement (iii): `(-18)/(13)` lies to the left of 0 on the number line.**

1. **Identify the value:**
- `-18/13` is a negative number (approximately -1.38).

2. **Determine its position on the number line:**
- Negative numbers lie to the left of 0.

**Conclusion for Statement (iii):** Since `-18/13` is negative, it does lie to the left of 0. Thus, the statement is **True (T)**.

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

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