For this question you may type your answer, but you are encouraged to show work Write an expression logically equivalent to the provided expression below using only the following logical connectives (negation, conjunction):  ¬ , ∧ {“version”:”1.1″,”math”:”\neg, \wedge “} Provided expression:  ¬ p ∨ r {“version”:”1.1″,”math”:”\neg p \vee r”} It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

Determine whether the following is a tautology, a contradiction, or neither, and justify your answer with a truth table. Make sure to explain how the truth table does indeed show that your answer is correct, and make sure to show the intermediary steps in your truth table.  For your uploads: please label the file with your name, and some indication of which problem it is (not the problem number, but something about the problem. The problems are shuffled so not everyone has the same number). ((p ∨ q) ∧ ¬p) → q It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

Which of the following are equivalent to the statement: if r, then s.  Select all that apply

Identify the contrapositive of  r → s {“version”:”1.1″,”math”:”r\rightarrow s “}

OPTIONAL: If you want the possibility of partial credit for wrong answers to the other question on this page, upload your work or give your rationale here. You are also welcome to upload an audio explanation. Please ensure that any attachment is upright and legible.  It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know.

The table below shows the values of predicate P(x,y) for every possible combination of values of the variables x and y. The row number indicates the value for x, and the column number indicates the value for y. The domain is {1,2,3}.  P y=1 y=2 y=3 x=1 F F T x=2 T T T x=3 F T F Do the following: (i) Indicate whether each of the following statements is true or false. (ii)  If false, then provide a negation of the statement that’s as simple as possible (i.e., move the negation as far inside the parentheses as possible).  Don’t forget the negation(s)! part a: ∀ x ∃ y P ( x , y ) {“version”:”1.1″,”math”:”\forall x \exists y P(x,y)”} part b:  ∃ y ∀ x P ( x , y ) {“version”:”1.1″,”math”:”\exists y\forall x P(x,y) “} part c: P ( 2 , 3 ) {“version”:”1.1″,”math”:”P(2,3)”} part d:  ∀ y P ( 2 , y ) {“version”:”1.1″,”math”:”\forall y P(2,y) “} If you want partial credit for incorrect answers, then explain your answers and how you got them, thoroughly.  It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

Which of the following expresses (something equivalent to) the negation of the statement “Everyone who passed the final also passed the course”? Assume that not passing is the same as failing. It is recommended you try to think of the answer before reading through the multiple choice options. 

Which of the following are propositions? Assume that Q(x) and R(x) and predicates, and that the domain is the set of positive integers. Select all the apply.

OPTIONAL: If you want the possibility of partial credit for wrong answers to the other question on this page, upload your work or give your rationale here. You are also welcome to upload an audio explanation. Please ensure that any attachment is upright and legible.  It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”).  For your uploads: please label the file with your name, and some indication of which problem it is (not the problem number, but something about the problem. The problems are shuffled so not everyone has the same number).

What are simple substances which cannot be decomposed by ordinary chemical means?