Are the following statements True or False? If they are True, prove them. If they are...

 

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Are the following statements True or False? If they are True, prove them. If they are False, show they are False using at least one example or contradiction: 1000n + 20 = o(n²) 3n²+8n6= 0(n³) n5 = (11n² + 8n + 9) For all positive constants a>0, a' > 0, b>0, b'>0, t> 0, t'>0, we have an² + bn + t = 0(a'n² + b'n + t') 3n³ + 20n² = o(n³ + 7n) If f(n) = 0(g(n)) and g(n) = o(h(n)) then ƒ(n) ‡ 0(h(n)) If fi(n) = 0(g₁(n)) and f₂ (n) = 0(g₂ (n)) and f3(n) = 0(g3 (n)) f₁(n) + f₂(n) + ƒ3 (n) = 0 (max (g₁ (n), g₂(n), 93 (n))) If f₁(n) = 0(g₁(n)) and ƒ₂ (n) = 0(g₂(n)) then f₁(n) — ƒ₂ (n) = 0(g₁(n) — 9₂(n)) If f(n) = 0(g(n)), then 2f(n) = 0(29(n)) then: Are the following statements True or False? If they are True, prove them. If they are False, show they are False using at least one example or contradiction: 1000n + 20 = o(n²) 3n²+8n6= 0(n³) n5 = (11n² + 8n + 9) For all positive constants a>0, a' > 0, b>0, b'>0, t> 0, t'>0, we have an² + bn + t = 0(a'n² + b'n + t') 3n³ + 20n² = o(n³ + 7n) If f(n) = 0(g(n)) and g(n) = o(h(n)) then ƒ(n) ‡ 0(h(n)) If fi(n) = 0(g₁(n)) and f₂ (n) = 0(g₂ (n)) and f3(n) = 0(g3 (n)) f₁(n) + f₂(n) + ƒ3 (n) = 0 (max (g₁ (n), g₂(n), 93 (n))) If f₁(n) = 0(g₁(n)) and ƒ₂ (n) = 0(g₂(n)) then f₁(n) — ƒ₂ (n) = 0(g₁(n) — 9₂(n)) If f(n) = 0(g(n)), then 2f(n) = 0(29(n)) then:

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1 This statement is true lim n 1000n ... View the full answer