P2.3.N (10) In CS 187, you've encountered big-O notation. Consider two functions with natural arguments and positive real values: f,g NR+. Consider the following propositions, where c ranges over positive reals, and n, no range over the naturals: P : 3c : : yn : n f(n) cg(n) (this is the definition of "f(n) is O(g(n))") a) Are any two of these propositions equivalent, for arbitrary choices of f and g? (prove it, or give examples of f and g for which they differ). b) Is any of the propositions always true, whatever f and g? c) Can you find two functions f and g for which R is true? P2.3.N (10) In CS 187, you've encountered big-O notation. Consider two functions with natural arguments and positive real values: f,g NR+. Consider the following propositions, where c ranges over positive reals, and n, no range over the naturals: P : 3c : : yn : n f(n) cg(n) (this is the definition of "f(n) is O(g(n))") a) Are any two of these propositions equivalent, for arbitrary choices of f and g? (prove it, or give examples of f and g for which they differ). b) Is any of the propositions always true, whatever f and g? c) Can you find two functions f and g for which R is true