a) Using the formal definition of , prove that 3n³ + 2n² + n = (1000n² + 2000n + 3000).

b) Using the formal definition of , prove that 100nlogn + 50n = (50nlogn + 100n).

c) For each, state if it is true or false and briefly explain why:

if f(n) = O(g(n)) and g(n) = O(f(n)), then f(n) = g(n)

if f(n) = (g(n)) and g(n) = (h(n)), then f(n) = (g(n))

if f(n) = O(g(n)) and g(n) = O(h(n)), then h(n) = (f(n))

if f(n) = (g(n)) and f(n) = o(h(n)), then h(n) = (g(n))

f₁(n) = O(g₁(n)) and f₂(n) = O(g₂(n)), then f₁(n) x f₂(n) = O(g₁(n) x g₂(n))