2
votes
1answer
67 views

What is the difference between $Γ⊭Φ$ and $Γ⊭¬Φ$?

Did I understand this correctly? $Γ⊨Φ$ ($Φ$ is considered true) $Γ⊨¬Φ$ ($Φ$ is considered false) $Γ⊭Φ$ ($Φ$ is considered neither true nor false) $Γ⊭¬Φ$ ??? Please help me understand. How can ...
1
vote
1answer
83 views

Prove that $((p\lor q)\land(p\lor(\lnot q)))\rightarrow p$ is a tautology

Prove that $((p\lor q)\land(p\lor(\lnot q)))\rightarrow p$ Please could someone give me some feed back on this proof? Does it look correct? = $\lnot ((p\lor q)\land(p\lor(\lnot q)))\lor p$ = $ ...
1
vote
0answers
163 views

proof of validity of tautology in first order logic

Every first-order logic formula which has a tautological shape in propositional logic is a valid formula. Will it be possible to give a formal proof for the above ? Thanks and Regards.
0
votes
1answer
35 views

How can I progress this derivation?

I'm learning propositional calculus in a discrete mathematics course. I'm trying to kick the habit of using axioms like equations and now I'm a little stuck and could use a nudge. Using a compact ...
2
votes
1answer
82 views

Does this proof using Novikov axiomatic propositional logic hold?

This question seems absolutely elementary but I'm having a hard time completing the proof, in fact I may have taken a bit of a left turn on it or I may be improperly applying axioms all together. ...
1
vote
2answers
128 views

Predicate Logic Argument Validity

My question is whether or not the following is a validly structured argument: (P→T)→Q Q → ¬Q ∴ P I'm getting hung up on the Q→¬Q part by itself as a premise, it doesn't seem like that is ...
2
votes
3answers
200 views

Logical propositions, which one is true and how to write a short proof?

I am studying for an entrance exam. Now I am stuck on this question: Suppose that P, Q are propositions such that "P or Q" is true. For each proposition (1), (2) and (3) which of the following ...