Please help construct a proof (propositional logic)

[lostinspace89]

This is a two part question my book gives as practice problem. I, however am struggling to construct logical proofs and the book does not have a key. Thanks in Advance!


2a. Construct a proof, using any method (or rules) you want, that the following argument is valid:
Premises (3): – [A&B], – [B&C], A v C
Conclusion: – B
Be sure to explain your proof procedure.

2b. Construct a proof, using only the 10 basic (primitive) rules, that the same argument is valid.

 

[micromass]

Please post your attempt or this thread will be deleted.

 

[lostinspace89]

I do not understand the question enough to make a valid attempt as this is why I posted it in this forum...

 

[micromass]

Then you should read your textbook again or ask your instructor. We are not here to explain the theory to you. We are only here to guide you to finding a solution.

 

[lostinspace89]

Ok, thanks for your help.

Is there anyone out there willing to help guide me to finding a solution...

 

[micromass]

Ok, thanks for your help.

Is there anyone out there willing to help guide me to finding a solution...

We're happy to help you, as long as you make some attempt first.

 

[lostinspace89]

This is what I have so far. At this point I am unsure of where to go next:

-[A&B]

​

A
-[B&C]

​

A
[A v C]

​

A
-A

​

Line 1, &O
-[A v B]

​

Line 4, vI
-B

​

Line 2, &O
-[B v C]

​

Line 5, vI

 

[mtayab1994]

This is what I have so far. At this point I am unsure of where to go next:

-[A&B]

​

A
-[B&C]

​

A
[A v C]

​

A
-A

​

Line 1, &O
-[A v B]

​

Line 4, vI
-B

​

Line 2, &O
-[B v C]

​

Line 5, vI

You're tryingn to prove the negation of (A&B) ...

 

[lostinspace89]

Are you asking me if I am trying to prove the negation of (A&B)? I am trying to prove the conclusion -B

 

[mtayab1994]

Are you asking me if I am trying to prove the negation of (A&B)? I am trying to prove the conclusion -B

OK I didn't understand what you meant.

 

[lostinspace89]

I am not sure that the path I have chosen is correct. I feel like the entire question can be answered with one proof if that proof were to satisfy the requirements of question 2b. It could be applied as the answer to question 2a

 

[Redbelly98]

Thanks for showing an attempt.

This is what I have so far. At this point I am unsure of where to go next:

-[A&B]

​

A
-[B&C]

​

A
[A v C]

​

A
-A

​

Line 1, &O

I don't see how this follows from line 1. Line 1 implies (-A v -B), but not necessarily -A.

-[A v B]

​

Line 4, vI
-B

​

Line 2, &O
-[B v C]

​

Line 5, vI

Another approach would be to try proof by contradiction, also referred to as an indirect proof.