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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.
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.