All Questions
Tagged with symbolic-logic deduction
15
questions
-1
votes
2
answers
119
views
Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) [closed]
Prove that the following is a logical truth (tautology) using a natural deduction derivation:
(B → C) ˅ (¬B → C)
How do I prove this using statement logic? I know I need to start with a supposition ...
5
votes
1
answer
1k
views
Why does Gensler's Star Test not work on some syllogisms? [duplicate]
All teachers are intelligent.
All teachers are well-paid.
From the Star Test, we can deduce that the argument must be invalid with whatever conclusion (according to the classical syllogism figures), ...
user47471
1
vote
0
answers
87
views
Is there a semantically complete system of direct-method natural deduction/sequent calculus?
Does anybody know of a system of direct-method natural deduction/sequent calculus, in other words, a system that does not require (or even incorporate) conditional (and indirect) proof method(s) and ...
- 41
0
votes
3
answers
712
views
How to solve this natural deduction problem?
This one is driving me crazy. I don't understand most keys for de morgan, modus ponens, etc, so please abbreviate if possible? EX: DM, MP, SIMP, HS, Conj, Imp (material Implication). Thank you anybody ...
- 21
1
vote
2
answers
6k
views
How to get proof using proof editor and checker
How can I use Natural deduction proof editor and checker or The Logic Daemon to derive the given conclusion from the given premise:
(∃x) ( Fx ∙ (y) (Fy → y = x) )
/ (∃x) (y) (Fy ≡ y = x)
It tells me ...
- 289
2
votes
3
answers
2k
views
Deriving "(p.q) v (p.r) from "p.(q v r)"?
I am new to logic. and here are my tryouts for deriving deriving "(p.q) v (p.r) from "p.(q v r)", and further I want to show that ”p.(q V r)” is equivalent to ”(p.q) V (p.r)”, by using natural ...
- 33
2
votes
4
answers
531
views
In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)
Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)
I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
- 21
1
vote
2
answers
497
views
Predicate logic proofs - how to split a disjunction bound by two quantifiers
I need to complete the following proof using only primitive rules (the introduction and elimination rules for each connective and quantifier).
(∃x)(∀y)(Py ∨ Qx) ⊢ (∀y)Py ∨ (∃x)Qx
I've only been able ...
- 13
2
votes
3
answers
268
views
Logic question regarding a logical truth
Is the following logically true? ∃x[Cube(x) →∀yCube(y)]
I think that it is logically true. When translated into truth functional form we have: A→B. A truth table shows that it is not a tautology but ...
- 61
3
votes
1
answer
320
views
What are the rules for a zero-premise derivation involving disjunctions?
I'm having trouble with the following zero-premise deduction that involves two disjunctions:
The solution seems simple, but I'm unsure of how to proceed with the two disjunctions. If it were just ...
3
votes
4
answers
1k
views
Proof for the Rule of Absorption in Natural Deduction?
I know there is a "formal proof" in "natural deduction" for the "rule of absorption" that employs the "law of excluded middle". It is presented in Wikipedia (...
- 41
4
votes
2
answers
647
views
Implication Introduction formulated as a theorem?
While making a list of the rules of inference for my math students, I came across this list on Wikipedia:
I noticed a pattern: for every introduction rule, there seems to be an elimination rule, and ...
- 817
2
votes
2
answers
184
views
How to prove 1. ~(KvF) 2. ~F=>(KvC) 3. (GVC)=>~H / ~(KvH) using natural deduction
I need help with this question using the first 13 rules of inference. Here is what I have so far:
~(KvF)
~F=>(KvC)
(GVC)=>~H / ~(KvH)
~Kv~F DM 1
~Fv~K Com 5
3
votes
4
answers
4k
views
Anyone can help me with proving ~(AvB) |- ~(BvA) via natural deduction?
~(AvB)
ㅡㅡㅡㅡ
~(BvA)
I have to provide a derivation to establish validation of this argument.
First of all, can I first change ~(AvB) into ~A&~B by using the De Morgan rules?
And the second is:...
- 31
4
votes
2
answers
167
views
help with deductive proof
∀x (Fx ∨ x=c), ¬Fb ∧ Gb |- ¬Fa → Ga
So far I don't understand how to switch variables around to prove the result.
I've got a subproof set up assuming "¬Fa" in order to derive "Ga".
In that proof I ...
- 153