Need help on 3.5

Probtums3. Consider twoalgorithms A and B thattake time in O(n?) and OP), respectively. Could there exist an implementation of algorithm B that would be more efficient (in terms of computing time) than an implementation of algorithm A on all instances? Justify your answer Problem 3A, what does O (1) mean? 6(1)? Problem 3.5. Which of the following statements are true? Prove your answers 3, 2" E (2n+1) 4, ml e eun + D) Problem 3.6. Prove that if fime on) then IfnRe oun). Problem 3,.7. In contrast with Problem 36, prove that 2/im necessarily follow from f( n ) E O ( ) . 012") does not Problem 3.8. Consider an algorithm that takes a time in e(ns D to solve instances of size n. Is it correct to say that it takes a time in Oun1)? In 0in1 )? In e(n1")? Justify your answers. (Note: Ig3 1.58496 Problem 3.9. Prove that the O notation is refiexivefme of(n)) for any func