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Conditional Proof

created by Tem42

(idea) by Tem42 (20.6 hr) (print)   ?   (I like it!) Thu Nov 18 1999 at 14:26:57

A rule of interferance from propositional logic. CP for short.

If you have an argument with the conclusion in the form of a implication (logical operator, not rule of implication), you can assume the antecedent, and using that try to deduce the consequent. For example:

N>O
N>P
Therefore N>(O*P)

Assume N. (this is called aceptance of conditional proof(ACP))
Use Modus Ponens to derive O and P from the first two statements. Conjoin them with conjunction. You now have showen that if you have N, you have O*P.
N>(O*P)

See also:: Everything Logic Symbols, Disjuctive Syllogism, Double Negation, Tautology, DeMorgan's Rule, Modus Ponens, Hypothetical Syllogism, Constructive Dilemma, Conjunction, Commutativity,


Here's the whole thing...

1. F>E
2. (F*E)>R // F>R
| 3. F ACP
| 4. E MP 1,3
| 5. F*E Conj 3,4
| 6. R MP 2,5
7. F>R CP 3-6.


printable version
chaos

conjunction The Difference Between Explanation and Prediction Discard this message indirect proof
1+2+3+ ... +n : Proof by Picture reductio ad absurdum tyranny conditional
Constructive Dilemma COQ Soma propositional logic
tautology Commutativity 1=2 Everything logic symbols
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