1. (8 points) Asymptotic analysis is foundational in many disciplines in Computer Science. At the heart of asymptotic analysis is big-O notation. Definition1 on page 205 of big O notation can be written formally using quantifiers in the following way. Let f and g be functions from the set of integers to the set of real numbers. We say that f(x) is O(g(x)) if where the variables a and k are assumed to be over the set of integers and the variable C is over the real numbers) is, show that the proposition above evaluates to true when f()2r and g(x)2 That is, show that the proposition above evaluates to false when f(x) = 2 and g(x) = 2r. (a) Using this definition and our proof strategies for quantified statements, prove that 2r is O(r2). That (b) Using this definition and our proof strategies for quantified statements, prove that 2 is not O(2r)