Data structure and algorithms by Weiss Mark Allen

Question

Suppose T₁(N) = O(f(N)) and T₂(N) =O(f(N)). Which of the following are true?

a) T₁(N) + T₂(N) = O(f(N))

b) T₁(N) - T₂(N) = o(f(N))

c) T₁(N)/T₂(N) = O(1)

d) T₁(N) = O(T₂(N))

My solution:

a) true. let f1=n^2 and f2=n ,"a" option holds true.

b) false. f1=n^2 and f2=n, for both T=O(f(n^2)) and thus option "b" is false.

c) false. take f1 and f2 same as before. Then f1/f2=n ==> O(n).

d) false. take f1 and f2 same as before. Then T1(n) = ω(T2(n))

Am i doing it right ?

Comments

Yes.