Step 1: Understanding the Concept:
Turfgrasses are categorized into two major environmental classes based on their photosynthetic pathways and growth habits: warm-season grasses ($\text{C}_4$ pathway) and cool-season grasses ($\text{C}_3$ pathway).
Step 2: Detailed Explanation:
- Statement (I) is true: Cynodon dactylon (Bermuda grass Doob grass) is a highly resilient, fast-growing turfgrass.
It forms a dense, traffic-tolerant turf when regularly mown, making it the most preferred choice for lawns, sports fields, public parks, roadsides, and golf courses globally.
- Statement (II) is false: Cynodon dactylon, Stenotaphrum secundatum (St. Augustine grass), and Paspalum notatum (Bahia grass) are all tropical and subtropical warm-season grasses ($\text{C}_4$).
They thrive in temperatures between $25^{\circ}\text{C}$ to $35^{\circ}\text{C}$ and go dormant/brown during cold winters.
They are not cool-season grasses and are unsuitable for establishing lawns in cool or temperate climates.
Step 3: Final Answer:
Statement I is correct, but Statement II is incorrect.