Identify true or false statements. Correct each false statement to make it true.
(i) Number of species in a community really matter to the functioning of the ecosystem.
(ii) David Tilman proved that decreased diversity contributed to higher productivity.
(iii) Rich biodiversity is not essential for ecosystem health but required for survival of human race of earth.
(iv) Species which are dangerously harmful beings and their interests can be thought of deliberate extinction.

Answer

To solve the question, we need to evaluate each statement and determine whether it is true or false. If a statement is false, we will correct it to make it true.

### Step-by-Step Solution:

1. **Statement (i):** "Number of species in a community really matter to the functioning of the ecosystem."
- **Evaluation:** This statement is **True**. The number of species in a community does significantly impact the functioning of the ecosystem. A higher diversity of species often leads to better ecosystem resilience and productivity.

2. **Statement (ii):** "David Tilman proved that decreased diversity contributed to higher productivity."
- **Evaluation:** This statement is **False**. David Tilman actually demonstrated that **increased diversity** contributes to higher productivity.
- **Correction:** The corrected statement is: "David Tilman proved that increased diversity contributed to higher productivity."

3. **Statement (iii):** "Rich biodiversity is not essential for ecosystem health but required for survival of human race of earth."
- **Evaluation:** This statement is **False**. Rich biodiversity is indeed essential for ecosystem health as it supports various ecosystem services that are vital for both ecosystems and human survival.
- **Correction:** The corrected statement is: "Rich biodiversity is essential for ecosystem health and required for survival of the human race on Earth."

4. **Statement (iv):** "Species which are dangerously harmful beings and their interests can be thought of deliberate extinction."
- **Evaluation:** This statement is **True**. Species that are harmful can be considered for deliberate extinction if they pose a significant threat to ecosystems or human health.

### Final Summary of Statements:
1. True
2. False - Corrected to: "David Tilman proved that increased diversity contributed to higher productivity."
3. False - Corrected to: "Rich biodiversity is essential for ecosystem health and required for survival of the human race on Earth."
4. True