For each of the following pairs of functions, either f(n) is in o(g( f(n) is in ω(g( or f(n) = θ(g( for each pair, determine which relationship is correct. justify your answer. (a) f(n) = log n2 ; g(n) = log n + 5. (b) f(n) = √ n; g(n) = log n2 . (c) f(n) = log2n ; g(n) = log n. (d) f(n) = n; g(n) = log n. (e) f(n) = n log n + n; g(n) = log n. (f) f(n) = log n2 ; g(n) = (log n)2 . (g) f(n) = 10; g(n) = log 10. (h) f(n) = 2n ; g(n) = 10n2 . (i) f(n) = 2n ; g(n) = n log n. (j) f(n) = 2n ; g(n) = 3n . (k) f(n) = 2n ; g(n) = nn .