Part I: Understanding logical expressions (30 pt.) (10 pt., 2 pt. each) Write each of the following conditional statements in the form "if p, then q" and state the corresponding converse, inverse, and contrapositive a. I will send you the address only if you give me the number b. Getting the job implies that you were the best candidate. c. It is necessary to have a valid password to log on to the server. d. A sufficient condition for the warranty to be good is that you bought the computer less 1. than a year ago. e. You will pass the course unless you do not complete the homework. 2. (10 pt., 2 pt. each) Let P(x) be the statement "x is a student" (x) be the statement "x is a professor," and R(x, y) be the statement "x asked a question to y." If the domain of x and y consists of all people, express each of the following sentences in terms of P(x), Q(x), R(x, y), quantifiers, and logical operators. n a. It is not the case that some student has never asked a question.ar ons yb. There is a professor who has never been sked a question by a student. c. Some student has asked every professor a question. d. There is a student who has asked a question to exactly one professor e. There are two different students who have asked each other a question. 3. (10 pt, 2 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