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Argument or Non-Argument?
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<br/> -Argument or Non-Argument? (6 points)<br/><br/><br/><br/> <br/>

-Acid rain is an ecological threat that must be taken seriously. Acid rain has killed the fish in thousands of lakes, and it has caused billions of dollars in damages to important crops. Furthermore, acid rain poses a serious threat to our nation's forests. 


-There are three familiar states of matter: solid, liquid and gas. Solid objects ordinarily maintain their shape and volume regardless of their location. A liquid occupies a definite volume, but assumes the shape of the occupied portion of its container. A gas maintains neither shape nor volume. It expands to fill completely whatever container it is in. 


-It really does matter if you get enough exercise. Studies show that exercise now helps you maintain independence as you age. Exercise also helps you to maintain muscle mass and plays a role (along with healthy eating) in maintaining a healthy weight.  






-Determine whether the following arguments are Inductive or Deductive. Then determine whether they are Valid/Invalid or Strong/Weak? (12 points)*** Be sure to use the correct evaluative word for the type of argument it is.





-Since Greenville is one mile from Central City, and Central City is one mile from Harristown, it follows necessarily that Greenville is two miles from Harristown. 


-All bachelors are men. No men are women. Therefore, no bachelors are women.


-The National Questioner (known for its sensationalist journalism) reports that a young boy in Oklahoma has spoken with Martians. Thus, we must draw the conclusion that Martians do indeed exist. 




-Most of the students attending Shoreline Prep have extremely wealthy parents. Since Madeline is a student at Shoreline, it is likely that her parents are wealthy. 










-Use a truth table to determine if the following statement is tautologous, contradictory, or contingent. Show your work. (8 points)


-(P  &gt;   Q)   &gt;   [P   &gt;  (P   &amp;   Q)]








-Use a truth table to determine if the following pairs of symbolized statement are logically equivalent, contradictory, consistent or inconsistent. (8 points)


-P  &gt;  Q /  (P  v  P)  &gt;  Q 






-Translate the following argument and then use a truth table to determine if it is valid/invalid. Use the bold words as letters. (10 points)


-Either clients will be disturbed or will leave, if they have to wait more than five minutes. Clients will not leave. So if they have to wait more than five minutes, they will be disturbed.
























-Translate the following statements into propositional logic. Use the bold words as letters. (2 points each, 8 total)


-John and April do not smoke in restaurants if smoking in restaurants is illegal.


-John and April smoke in restaurants only if smoking in restaurants is legal.


-Neither April nor May drive under the influence but John does.


-April sings pop music and May and John sing country music.












-Construct a formal proof for each of the following valid arguments using the first 8 rules. (rules of implication/inference) (4 @ 8 points each, 32 total)


-

-A &gt; [(B v D) &gt; (S &amp; R)]
-A &amp; L
-B &amp; X
-S &gt; (~T &amp; V)
-T v P          / P                                                  









-

-(~A &amp; D) &gt; ~E
-~A &amp; C  
-A v B
-B &gt; D
-E v (E v G)  / G






-  Hint: uses CD
-R &gt; (M &gt; ~P)
-R &gt; (S &amp; Q)
-L v R
-~L
-S &gt; (C &gt; P)  
-M v C      / ~P v P





-A &gt; ~C
-A &amp; D
-(E &amp; B) &gt; C
-(E &amp; B) v F
-F &gt; (~C &gt; G)  / G






-Construct a formal proof for each of the following valid arguments using the rules of implication/inference and the first 5 rules of replacement. (8 points each, 16 total)




-       
-R &gt; ~X
-D v R
-X      /D


-   
-~(~E v ~N) &gt; T
-G &gt; (N &amp; E)     /G &gt; T











EXTRA CREDIT: 5 points
Construct a proof for the following valid argument using all 18 rules



-(A &amp; B) &gt; C
-(B &gt;C) &gt; (Q v X)
-~(Q v ~A)       /X 

Step-by-step answer

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Subject: Logic, Math

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