Question

Q4 Let F denote a countably infinite set of functions such that each f; e F is a function from Z+ to R+, and let R be a homogeneous binary relation on F where R = {(fa, fb) | fa(n) € (fo(n))}. Prove that R is a reflexive relation. In your proof, you may not use a Big-12, Big-0, or Big- property to directly justify a relational property with the same name; instead, utilize the definition of Big-12, Big-O, and Big-O.

Answer 1

zno. This proves that so): fon) = fch) to any nezt i.e any nelTherefore To prove that Ra{ba,toll-fum) E O C£,(n))}. is reflexive, prove that (ff) ER for my fff ief f:2 Rt Hence need to prove that f= O(f) for any fiat ort, as per the definition of Big-6, this entails proving that f= 0(4), fS-2CP) To prove that f= o(f) Consider C=1, 2=1. Then, as fch) & CR(h) for any f = oct) neztie Similarly fol fath(4), consider C=1, no=1.then, n21, therefore as f(n) = f(n) for any any fen) ze. (n) fol any nz no. this proves that f = 2(f) Hence, the two Statements together prove that f = e(t). Therefore, the relation is reflexive, and the proof is compute. Thank you.. **t please give me a like txt