Question 1:

ASSIGNMENT PURPOSE The purpose oi this assignment is to help you apply the concepts learned in the lesson to prepare you for the student learn outcome: Write proofs using symbolic logic, Boolean algebra, and mathematical induction. Additionally, the peer review process gives you a structured way to learn how to critique the validity of another individuals argument, and it provides me with evidence of regular student-to-student contact in the course. Do not inciude your name of this document, so the peer-review process can be as anonymous as possible. As long as you upload this assignment through your Canvas account, then your work will be connected to your name for grading purposes. I have set the peer review parameters in Canvas to be anonymous. Problem 3.13 Prove that the propositional formulas PvaR and (PnQ)v (QAuR)V(RA .P) V (PAQAR) are equivalent. Problem 3.45 The following predicate logic formulas is invalid: Vx,3y.P(x,y) =9 Ely,Vx.P(x,y) Indicate which of the following are counter models for this formula and briey explain your reasoning. (a) The predicate P(x,y) ::= y -x = l where the domain of discourse is Q. (h) The predicate P(x,y) ::= y