A binary tree is full if all of its vertices have either zero or two children. Let Bn denote the number of full binary trees with n vertices.

(a) By drawing out all full binary trees with 3, 5, or 7 vertices, determine the exact values of B3, B5, and B7. Why have we left out even numbers of vertices, like B4?

(b) For general n, derive a recurrence relation for Bn.
(c) Show by induction that Bn is (2n). 2.14. You are given an array of n elements, and

Write the command that can be used to answer the following questions. (hint: try each out on the system to check your results.) a. find all files on the system that have the word test" as part of their filename. b. search the path variable for the pathname to the awk command. c. find all files in the /usr directory and subdirectories that are larger than 50 kilobytes in size. d. find all files in the /usr directory and subdirectories that are less than 70 kilobytes in size. e. find all files in the / directory and subdirectories that are symbolic links. f. find all files in the /var directory and subdirectories that were accessed less than 60 minutes ago. g. find all files in the /var directory and subdirectories that were accessed less than six days ago. h. find all files in the /home directory and subdirectories that are empty. i. find all files in the /etc directory and subdirectories that are owned by the group bin."

Write a program that has a conversation with the user. the program must ask for both strings and numbers as input. the program must ask for at least 4 different inputs from the user. the program must reuse at least 3 inputs in what it displays on the screen. the program must perform some form of arithmetic operation on the numbers the user inputs. turn in your .py file as well as a screenshot of your program's output. include comments in your code to explain how it works an example program run might look like (have fun with this and be creative): ‘what is your name? ’ “josh” ‘, josh. what is your favorite color? ’ “green” ‘mine too. do you also like ice cream? ’ “no” ‘josh, how old are you? ’ “40” ‘ and how many siblings do you have? ’’ “3” ‘that means you are one of 4 kid(s). is green the favorite color of anyone else in your house? ’

Two students are discussing the flow of electricity. student a says that voltage is a measure of the amount of electron flow in a circuit. student b says that power is the product of voltage and current. which of the following statements is correct? a. only student a is correct b. only student b is correct c. both of the two students are correct d. neither of the two students is correct