Derivation of (P conditional Q) v P in System SD+

In summary, the problem is to show that (P conditional Q) v P is a theorem of system SD+. This means that we need to prove that the statement "If P then Q, or P" is always true in system SD+. To do this, we can create a truth table with four rows, representing all possible combinations of P and Q. By using the definition of the conditional statement and the logical rule of disjunction, we can show that in all four cases, the statement (P conditional Q) v P is true, thus proving it as a theorem in system SD+.
  • #1
Brcummings
1
0
Do a derivation showing that (P conditional Q) v P is a theorem of system SD+

*Sorry guys, I can't figure out how to do the symbol in between (P Q), but it means If P then Q and it is otherwise known as the conditional

-I am really struggling with this problem and I would greatly appreciate any help
 
Physics news on Phys.org
  • #2
Brcummings said:
Do a derivation showing that (P conditional Q) v P is a theorem of system SD+

*Sorry guys, I can't figure out how to do the symbol in between (P Q), but it means If P then Q and it is otherwise known as the conditional

-I am really struggling with this problem and I would greatly appreciate any help
What is system SD+?

Make a truth table with separate columns for P, Q, [itex]P \Rightarrow Q[/itex], and [itex]P \Rightarrow Q \vee P[/itex]

You need four rows.

To see how I got the "implies" arrow or the V, double-click the expressions that use these symbols, and another window with the LaTeX code opens.
 

1. What is the derivation of (P conditional Q) v P in System SD+?

The derivation of (P conditional Q) v P in System SD+ is a logical proof that shows how the statement (P conditional Q) v P can be derived or deduced from the axioms and rules of System SD+. It is a way of showing that this statement is true based on the principles of deductive reasoning.

2. What is System SD+?

System SD+ is a logical system or formal proof system that is used in mathematical and philosophical reasoning. It is an extension of the classical propositional logic system called System SD, which was developed by Gerhard Gentzen in the early 20th century. System SD+ allows for more complex and powerful proofs, and is often used in the study of modal logic and modalities.

3. How does the derivation of (P conditional Q) v P in System SD+ work?

The derivation of (P conditional Q) v P in System SD+ follows a set of well-defined rules and axioms. These rules and axioms allow you to manipulate logical statements and make deductions based on their logical structure. By applying these rules and axioms in a systematic way, you can construct a proof that shows the statement (P conditional Q) v P can be derived from the given premises.

4. What is the significance of (P conditional Q) v P in System SD+?

The statement (P conditional Q) v P is significant in System SD+ because it is a logical formula that captures the concept of conditional or hypothetical statements. It is also known as the principle of explosion or ex falso quodlibet, which means that if a contradiction can be derived from a set of premises, then any statement can be deduced from those premises. This principle is important in understanding the logical consequences of contradictory statements.

5. Are there any other systems or methods for deriving (P conditional Q) v P?

Yes, there are other systems and methods for deriving (P conditional Q) v P, such as natural deduction, truth tables, and semantic tableaux. Each of these approaches has its own set of rules and procedures for constructing logical proofs. However, System SD+ is a particularly useful system for deriving (P conditional Q) v P because of its ability to handle modalities and other complex logical concepts.

Similar threads

I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
    • Calculus
Replies
9
Views
853
Logic: proof that [p -> (q ^ r)] <=> [(p ^ -q) -> r]
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Dynamical Systems: how to find equation for Poincare map?
    • Calculus and Beyond Homework Help
Replies
1
Views
985
I Translate compound proposition p → q (implication) to p↓q question
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
873
Calculate y^(p+q) using the Leibniz formula
    • Calculus and Beyond Homework Help
Replies
12
Views
2K
If a and b are both quadratic residues/nonresidues mod p & q
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Prove One but not both of these systems is consistent.
    • Calculus and Beyond Homework Help
Replies
1
Views
910
Equivalence of Implications: P, Q, and R
    • Calculus and Beyond Homework Help
Replies
2
Views
3K
Dynamical Systems - Chaos: Stability condition for a 2-cycle system
    • Calculus and Beyond Homework Help
Replies
2
Views
834
Find Derivative: dp/dq if p = 1/(√q+1)
    • Calculus and Beyond Homework Help
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top