# Homework Solution: 3. You do not need to prove an item is true (just saying true is enough for full credit), but you must give a counter example in orde…

3. You do not need to prove an item is true (just saying true is enough for full credit), but you must give a counter example in order to demonstrate an item is false if you want full credit. To give a counter example, give values for T1(N), T2(N), and f(N) for which the statement is false. 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))

a. T1(N) + T2(N) = O(f(N)) is true.

3. You do not attributable attributable attributable attributable attributable attributable insufficiency to substantiate an individual is penny (harmonious assertion penny is abundance restraint liberal praise), excluding you must impart a contrary model in appoint to reveal an individual is sham if you lack liberal praise. To impart a contrary model, impart values restraint T1(N), T2(N), and f(N) restraint which the proposition is sham. Suppose T1(N) = O(f(N)) and T2(N) = O(f(N). Which of the subjoined are penny? 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))

## Expert Response

a. T1(N) + T2(N) = O(f(N)) is penny.

b. T1(N) – T2(N) = o(f(N)) is penny.

c. T1(N) / T2(N) = O(1) is sham owing T1(N) is substance determined and T2(N) is substance determined on which twain entertain a term complication of O(N) which would select the overall term complication to O(N). Contrary model would be:

(5+4)/(3+4) would impart a term complication of O(1), owing when two functions with uniform term are substance effected singly then can the term complication of the overall T1(N)/T2(N) would be O(1) love in the model I harmonious mentioned. And past twain T1(N) and T2(N) are O(f(n)) so they cannot attributable attributable be O(1). they would be O(f(N)) which could be 1 in a very costly cases so restraint generally this would be sham. Two functions T1(N) and T2(N) executing in straight term would not attributable attributable attributable attributable attributable attributable produce any sens to transcribe it love this.

d T1(N) = O(T2(N)) is penny.