CS 151: Mathematical Foundations of Computing Homework Assignment 01 Spring 2020 Instructions This assignment is due Monday, February 03, at 11:59PM (Central Time). This assignment must be submitted on Gradescope. Handwritten submissions are allowed as long as they are legible. Submissions typed in LaTeX or Word are preferred. Each question (1-6) must be answered on a separate page with answers for each sub-question (a-e) clearly labelled. A 5-point penalty will be applied to submissions that do not follow these guidelines. For more instructions on how to submit assignments on Gradescope see this guide Late submissions will be accepted within 0-12 hours after the deadline with a 5-point penalty and within 12-24 hours after the deadline with a 20-point penalty. No late submissions will be accepted more than 24 hours after the deadline. This assignment is individual. Offering or receiving any kind of unauthorized or unacknowledged assistance (including searching for solutions online is a violation of the University's academic integrity policies, will result in a grade of zero for the assignment, and will be subject to disciplinary action. Part 1: Understanding logical expressions (40 pt.) 1. (10 pt., 2 pt. each) Write each of the following conditional statements and the corresponding converse, inverse, and contrapositive as English sentences in the form "if p, then q." Example: I will pass the course if I come to class. Answer: Original statement: If I come to class, then I will pass the course. Converse: If I pass the course, then I will come to class. Inverse: If I do not come to class, then I will not pass the course. Contrapositive: If I do not pass the course, then I will not come to class. a. Getting the job implies that you were the best candidate. b. The cherry trees bloom when it stays warm for a week. c. Having a winning ticket is sufficient to win the prize. d. The nondisclosure agreement is valid only if you signed it. e. To access the network, it is necessary to have a valid password. 2. (15 pt., 3 pt. each) Determine the truth value of each of the following statements if the domain consists of all integers. If it is true, find a domain for which it is false. If it is false, find a domain for which it is true. Justify your answer. Example: Vx(x -2. True when the domain consists of all nonnegative integers. For all nonnegative integers x, XS 2x. a. Vx(x +1