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  3. 4 20 pts write true or false to each of...

Question: 4 20 pts write true or false to each of...

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4. (20 pts) Write true or false to each of the following statements (a) If f(n)-nt 8, then f(n) E 6( ) (b) If f(n)-㎡ +8, then f(n) E 0(n*) (c) If f(n)-ΣΑ l, then f(n) 0(log n) (d) If f(n)-ΣΑ , then f(n) E 0(n log n) (e) If f(n) - f(n) E (n) (f) If f(n) E O(n) and g(n) E O(n), then f(n) +g(n) E O(n) (g) If f(n) E 0(n) and g(n) E 0(n2), then f(n) + g(n) E O(n2) (h) If f(n) EO(n) and g(n) E O(n2), then f(n) +g(n) E O(n) (i) If f(n) E 0(n) and g(n) E Ω(n), then f(n) + g(n) E Θ(n) G) If f(n) E O(n), then n2 x f(n) E O(n) (k) If f (n) E O(n) and g(n) E O(n2), then f(n) x g(n) E O(n) (1) If f(n) E (nlogn), then f(n) X nE O(n2 log n) (m) lf f(n) E Θ(n log n) and g(n) E Θ(n logn), then f E Θ(1) (n) lf f(n) 0(n) and g(n) 0( 2), then linn )*)(n-0 (o) lf f(n) 62(n) and g(n) E Ω(n), then g(n) -Θ1 (p) If f(n) E e(m) and g/n) E (2), then li0 (q) If f(n) E Θ(n) and g(n) E Θ(n), then器 Θ1. (r) lf f(n) E 0(n) and lim n oo -0, then gin) E Ω(n) (s) If f(n) Θ(n) and lim, 100 g(r1-0, then g(n) Ω(n) (t) f(n)+g(n) E Θ(max f(n), g(n)) Ili >00 g(n) g(TI) 00 g(n n)

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