Let P(x, y) be a binary predicate where the type of x is A and the type of y is B. We define the projection π1(P) to be the unary predicate on A defined as follows: π1(P)(x) is true if and only if there exists an element y of B such that P(x, y) is true. Similarly, π2(P) is the unary predicate on B defined so that π2(P)(y) is true if and only if there exists an element x of A such that P(x, y) is true. a. Let A = B = {0, 1, 2, 3} and define P(x, y) to mean "x < y". Describe π1(P) and π2(P) as both predicates and relations.
b. What can you say about the predicate P if you know that π1(P) and π2(P) are each always false? What if they are each always true?
c. Suppose you are given a boolean method isInP(int x, int y) where each of x and y are restricted to the range from 0 through LENGTH - 1. Write boolean methods that will return the value of the predicates π1(P) and π2(P), given appropriate input

Read the following scenario, and then answer the question below. you want to send an e-mail to your boss requesting a meeting to discuss a raise. what is the best example of an e-mail to an employer about this meeting? “hey jason. can we chat about getting me more money soon? let me know. peace, meg.” “hello jason. pardon me for sending yet another e-mail today about my need to talk to you about my position and a possible pay increase. i am dying to know when you can talk. sincerely, meg.” “hello jason. i have been with the company for one year and have taken on more responsibilities than outlined in my job description. i would appreciate an opportunity to speak with you about my position. let me know when we can schedule a meeting. you, meg.” “greetings jason! i hope this e-mail finds you well and happy today. i really, really want to talk to you about something important. i am not sure if you have time. i hope you do. get back in touch with me and let me know when we might talk. ever so much for taking the time to read this. sincerely, meg.”