(Solved): There are 3 questions, worth a total of 30 points. Whenever possible, use logic laws to simplify yo ...

There are 3 questions, worth a total of 30 points. Whenever possible, use logic laws to simplify your answer. Question 1. Compound Statements (5 Points) Let

"John is healthy",

"John is wealthy", and

"John is wise". Write the sentence "John is healthy and wise, but is not wealthy." as a compound proposition in symbolic form. Question 2. Arguments and Argument Forms (10 Points) Show, by constructing a truth table, that the following inference rule is valid. Indicate which column(s) are for the premises, which column is for the conclusion, and which row(s) are critical rows.

Question 3. Conditional/Quantified Propositions and Their Negation (15 Points) 3.1) The negation of the conditional statement

is (Show your steps below) 3.2) Write symbolically the following statement and its contrapositive: "If a graph has an odd cycle, it is not two-colorable" (You have to come up with your own predicates.)