For each of the following purported properties related to symmetry, decide whether you think the statement is true or false, and—in either case—prove your answer 1. Prove or disprove: if f(n) =...

For each of the following purported properties related to symmetry, decide whether you think the statement is true or false, and—in either case—prove your answer

1. Prove or disprove: if f(n) = Ω(g(n)), then g(n) = Ω(f(n)).

2.Prove or disprove: if f(n) = Θ(g(n)), then g(n) = Θ(f(n)).

3.Prove or disprove: if f(n) = ω(g(n)), then g(n) = ω(f(n)).