is there anyone can do question #7 ? thanks a lot.

COMP 2804 — Assignment 2Due:Wednesday October 19, before 4:30pm, in the course drop box in Herzberg 3115.Assignment Policy:Late assignments will not be accepted. Students are encouraged tocollaborate on assignments, but at the level of discussion only. When writing the solutions,they should do so in their own words. Past experience has shown conclusively that thosewho do not put adequate effort into the assignments do not learn the material and have aprobability near 1 of doing poorly on the exams.Important note:When writing your solutions, you must follow the guidelines below.•The answers should be concise, clear and neat.•When presenting proofs, every step should be justified.•Assignments should be stapled or placed in an unsealed envelope.Substantial departures from the above guidelines will not be graded.Question 1:On the first page of your assignment, write your name and student number.Question 2:The functionf:N→Nis defined byf(0) = 1,f(n) =12·4n·f(n-1) ifn≥1.Prove that for every integern≥0,f(n) = 2n2;this reads as 2 to the powern2.Question 3:The functionsf:N→Nandg:N2→Nare recursively defined as follows:f(0)= 1,f(n)=g(f(n-1),2n)ifn≥1,g(0,n)= 0ifn≥0,g(m,n) =g(m-1,n) +nifm≥1 andn≥0.Solve these recurrence relations forf, i.e., expressf(n) in terms ofn. Justify your answer.Hint:Start by solving the recurrence relation forg.1

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