Solve Messy Logic Problem | Hayden Kee

  • Context: Undergrad 
  • Thread starter Thread starter hayden_kee
  • Start date Start date
  • Tags Tags
    Logic
Click For Summary

Discussion Overview

The discussion revolves around a logic problem involving propositional logic and the validity of an argument. Participants are exploring different assumptions and derivations to reach a conclusion based on the given premises.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Hayden Kee expresses difficulty in solving a logic problem and seeks assistance.
  • One participant asks for clarification on whether the goal is to determine the validity of the argument and suggests testing specific truth values for A, B, C, and D.
  • Hayden later describes a method of deriving a conclusion by assuming B and C to be true, leading to the conclusion that D must be false and ultimately showing that A is the result.
  • Another participant shares a similar approach, detailing their derivation steps but struggles to conclude A from the C sub-derivation.

Areas of Agreement / Disagreement

Participants are exploring different methods to derive conclusions from the premises, but there is no consensus on the final outcome or the correctness of the approaches taken.

Contextual Notes

Participants have not resolved how to derive A from the C sub-derivation, indicating potential gaps in their reasoning or assumptions.

hayden_kee
Messages
2
Reaction score
0
Hi,

Really struggling with this logic problem, would be very grateful to anyone willing to help

A v D
(~B ^ ~C) <==> D
B ==> ~(C ==> A)
---------------------
~B

Thanks in advance

Hayden Kee
 
Mathematics news on Phys.org
What exactly do you want to do? Determine whether or not the argument is valid?

What happens if you take A true, B true, C false, and D false?
 
trying to derive the conclusion
I did eventually work it out by assuming B and C to be true, after which I was able to show that D must be false, which allowed me to Eliminate the D v A disjunction showing that A is the result either way. Therefore I was left with C==>A which proved that my assumption of B must be false because of the third premise.

Thanks,

Hayden
 
I've also assumed B and C, with the C sub-derivation ending with A, and the final three lines of the B sub-derivation ending with the following:
W| C => A
X| B => ~(C =>A)
Y| ~(C =>A)

This allows ~I for the conclusion of ~B through the B assumption (line 4), and the contradictory pair on lines W and Y:

Z| ~B 4, W, Y, ~I

What I can't figure out is how to get A on the C sub-derivation. :S
 

Similar threads

Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K