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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

`p=`

"John is healthy",

`q=`

"John is wealthy", and

`r=`

"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.

`[[,pvvq],[,notq],[:.,p]]`

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

`(p^(^())q)=>notr`

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.)