For given functions f and g, define two additional functions:

h1(n) = max(f(n), g(n)) h2(n) = f(n) + g(n)

(a) show that h1(n) is o(h2(n)) (b) show that h2(n) is o(h1(n))

Write a program that prompts the user to input a string. the program then uses the function substr to remove all the vowels from the string. for example, if str = "there", then after removing all the vowels, str = "thr". after removing all the vowels, output the string. your program must contain a function to remove all the vowels and a function to determine whether a character is a vowel.

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