Need practice problems help

  • #1
I have about 10 questions, I hope someone can take the time to help me with. The directions are: "Use the 18 rules of inference, supply a proof for each of the following arguments." So, here goes:

1.) 1. (R v X) > (A > B)
2. ~ Q > ~ C
3. ~ C > Z
4. R .Y
5. Q v A /Z v B

2.) 1. E . (P . B)
2. (E . B) >~ (P.~M) /E.M

3.) 1. ~(S v C)
2. ~(S . R) > (C v D) /D

4.) 1. D > P /(I . D) > P

5.) 1. P v (Y . H)
2. (P v Y) >~ (H v C)
3. (P .~ C) > (K . X) /X v T

6.) 1. A = J
2. A v J
3. A > (J > W) /W

7.) 1. ~Q> (C . B)
2. ~T> (B . H)
3. ~(Q . T) /B

8.) 1. (U . P) >Q
2. ~ O > U
3. ~ P > O
4. ~ O . T /Q

9.) 1. (J>K) . (~O>~P)
2. (L > J) . (~M>~O)
3. ~K> (L v~ M)
4. ~K . G /~P

10.) 1. (F . M) > (S v T)
2. (~S v A) > F
3. (~S v B) > M
4. ~S . G /T

Okay, that's all the questions. Now here is the legend key:
/ separates what the conclusion is supposed to be.
. conjunction
v disjunction
> implication
= biconditional
~ negation

This is for an introductory to logic class. I hope someone can help. Thank you.
 

Answers and Replies

  • #2
honestrosewater
Gold Member
2,105
5
1.) 1. (R v X) > (A > B)
2. ~ Q > ~ C
3. ~ C > Z
4. R .Y
5. Q v A /Z v B
I read that as:
1. (R v X) > (A > B)
2. (~ Q) > (~ C)
3. (~ C) > Z
4. R .Y
5. Q v A
C. Z v B
By my calculations, this argument is invalid. Counterexample: (R, Y, C, Q) are true and (Z, B, A) are false (X is true or false). Did you copy it correctly? How are you grouping negations?
 
  • #3
honestrosewater
Gold Member
2,105
5
Here are some hints for the next three to get you started.
2) Can you derive ~(P . ~M)?
3) Can you derive (~S v ~R)?
4) Do you have the rule: ((P . Q) > R) = (P > (Q > R))?
 
  • #4


honestrosewater said:
I read that as:
1. (R v X) > (A > B)
2. (~ Q) > (~ C)
3. (~ C) > Z
4. R .Y
5. Q v A
C. Z v B
By my calculations, this argument is invalid. Counterexample: (R, Y, C, Q) are true and (Z, B, A) are false (X is true or false). Did you copy it correctly? How are you grouping negations?
Yes I did copy it correctly. This is directly from my teacher, too. I don't think he feels it's invalid. And, the ones that you put parentheses around, he didn't. I don't know if that matters or not. I really don't get anything about this class at all. As far as how am I grouping negations, I have no idea on that either. Thanks.
 
  • #5
honestrosewater
Gold Member
2,105
5
completely lost said:
Yes I did copy it correctly. This is directly from my teacher, too. I don't think he feels it's invalid.
Well, regardless of what he may feel, I checked it again, and it is invalid. Do you know how to check an argument for validity?
And, the ones that you put parentheses around, he didn't. I don't know if that matters or not. I really don't get anything about this class at all. As far as how am I grouping negations, I have no idea on that either. Thanks.
I added the parentheses to make clear what was being negated.
If you have no idea what you're doing, there isn't much I can do for you today. If you have a problem understanding something specific, I'll try to help. But we don't do people's homework for them here, so you'll have to put in some effort.
 

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