Weak Induction (1) Using weak induction, prove that 3" < n! for all integers n > 6.
(2) Prove that log(n!) < n log(n) for all integers n > 1.
Reminder 1: log(1) = 0.
Reminder 2: log(a*b) = log(a) + log (6).
Reminder 3: If a < b then log(a) < log(6).
Note: The base of the logarithms doesn't matter for any of the above.
(3) Prove for all integers n > 1 that if A1, A2, ..., An and B are sets, then:.
(A1∩A2∩...∩An)UB = (A1UB)∩(A2UB)∩...∩(AnUB)
Hint: Use the fact that (XNY) UZ = (XUZ)n(Y UZ) where X, Y, and Z are sets.

In this lab, you complete a prewritten c program that calculates an employee’s productivity bonus and prints the employee’s name and bonus. bonuses are calculated based on an employee’s productivity score as shown below. a productivity score is calculated by first dividing an employee’s transactions dollar value by the number of transactions and then dividing the result by the number of shifts worked.

Select the correct answer. andy received a potentially infected email that was advertising products. andy is at risk of which type of security threat? a. spoofing b. sniffing c. spamming d. phishing e. typo-squatting

Write a grading program for a class with the following grading policies: a. there are two quizzes, each graded on the basis of 10 points. b. there is one midterm exam and one final exam, each graded on the basis of 100 points. c. the final exam counts for 50% of the grade, the midterm counts for 25%, and the two quizzes together count for a total of 25%. (do not forget to normalize the quiz scores. they should be converted to a percentage before they are averaged in.) any grade of 90 or more is an a, any grade of 80 or more (but less than 90) is a b, any grade of 70 or more (but less than 80) is a c, any grade of 60 or more (but less than 70) is a d, and any grade below 60 is an f. the program will read in the student’s scores and output the student’s record, which consists of two quiz and two exam scores as well as the student’s average numeric score for the entire course and final letter grade. define and use a structure for the student reco