Give a recursive definition for each of the following. (You don’t need to prove your definitions are correct.) a) The function f(n) = 9n+3, n ≥ 1. b) The function f(n) = n^2 +n, n ≥ 1. c) The set S= {1, 1/2 , 1/4, 1/8,.....}

Find a possible function f ( n ) from the set of natural numbers to the set of natural numbers that corresponds to the sequence 7, 11, 15, 19, ... .  Then find the sum of the first 20 terms of that sequence.

Please help me with these question. I am having trouble understanding what to do. Please show all your work. Please do every question. I am study for my exam. And i need to know if I got the correct answer. And shown the correct steps Course: Discrete mathematics for CS Thank you

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Help me please

{1,5,10,15} and Y1 = {1,5,10,15,20}. Using the formal definition of a function, determine which of the following subsets of X1 × Y 1 correspond to the functions of X1 → Y 1. Justify your Problem 7. Let X1 = answer by providing reasons why each is or is not a function. 7(a) f = {(1,15),(5,10),(1,5),(10,1),(15,1)} 7(b) f = {(1,20),(5,1),(10,1),(15,5),(1,20)} 7(c) f = {(1,1),(5,1),(10,1)}