Please indicate whether the following statements are true or false. Explain in details why it is true or false.

1. n² log¹⁰⁰ n = O(n^2.01)

2. 13n^{log n} = (n log n)

3. If f(n) = O(g(n)) and g(n) = (h(n)) then f(n) = (h(n))

4. If f(n) = (g(n)) and g(n) = (h(n)) then f(n) = (h(n))

5. If f₁(n) = (g₁(n)) and f₂(n) = (g₂(n)) then f₁(n) + f₂(n) = (g_max(n)), where g_max(n) is the asymptotically larger function among g₁(n) and g₂(n).