please provide explaination for the solution and what the theorem is implying. Thank you in advance!

that is all the information provided!

Theorem 1.3 We have the following: fc implies g(n) (f(n)) if c > 0 = { o implies g(n) o(f(n)) o implies f(n) 0(g(n)) n-00 Proof: The proof is left as an exercise. Theorem 1.3 We have the following: c implies g(n) (f(n)) if c > 0 lim g(n) = { 0 implies g(n) o(f(n)) o implies f(n) (g(n)) Proof: The proof is left as an exercise. please provide explaination for the solution and what the theorem is implying. Thank you in advance