**THIS ASSIGNMENT IS DUE 3 HOURS FROM 12 PM Eastern Standard Time In USA.. NO EXCEPTIONS
**1. Consider the following open statements:**
**j(x) : Student x is a junior**
**p(x): Student x is a physics major**
**g(x): Student x is a graduate student**
**m(x): Student x is a mathematics major**
**Write each of the following statements in terms of quantifiers and the above open statements.**
**a). There is a mathematics major in the class who is a junior.**
**b). There is a graduate student in the class who is not a physics major.**
**c). No junior student in the class is a mathematics major.**
**d). Every junior in the class is majoring in either mathematics or physics.**
**2. Determine which of the following arguments are valid and which are invalid. Provide an explanation for each answer.**
** a). All mail carriers carry a can of mace.**
** Mr. Baker is a mail carrier.**
** Therefore Mr. Baker carries a can of mace.**
** b). All law-abiding citizens pay their taxes.**
** Mr. Brown pays his taxes.**
** Therefore Mr. Brown is a law-abiding citizen.**
**3. Suppose a,b,c and d are integers and a ¹c. Suppose also that x is a real number that satisfies the equation:**
**(ax + b) / (cx + d) = 1**
** Show that x is a rational number.**
1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done.
2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables):
a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment.
b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request.
3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement).