1. Consider the following pairs of functions. For each pair, state whether (i) f = Θ(g), (ii) f = O(g) but f ̸= Θ(g), (iii) g = O(f) but g ̸= Θ(f), or (iv) none of these.
a. f(n)=n,g(n)=2logn.
b. f(n)=n,g(n)=22logn.
c. f(n) = n2, g(n) = 1010n.
d. f(n)=2n,g(n)=2nlogn.
e. f(n) = nlog n, g(n) = (log n)n.
f. f(n) = n3 + 8n2 + 87, g(n) = n3/1000.
g. f(n) = 4n, g(n) = 3n.
h. f(n) = logn, g(n) = loglogn.
i. f(n)=nwhennisodd,f(n)=n2 whenniseven;g(n)=nwhenniseven,g(n)=n2
when n is odd.
j. f(n)=nwhennisodd,f(n)=n2 whenniseven;g(n)=n2.
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