Management Entrance Examination—Logic—Formal Logic—Summary—Knowledge Breakthrough—Formal Logic—Collection & Selection & Hypothesis—Contradiction

angle

Angle - summary - continuous optimization

1. Property
   (1) $AllSareP$ and$SomeSare\; notP$ contradiction
   (2)$AllSare\; notP$ and$SomeSisP$ contradiction
   (3)$ThisSisP$ and$ThisSis\; not$ the negative proposition of the$P-$ contradiction
   (1):"not" + "property proposition", which is equivalent toremoving the previous "not"and then changing the original nature proposition as follows:affirmation becomes negation, negation becomes affirmation; Everything becomes something, and something becomes everything.
   
2. Mode
   (1) $DefinitelyP$ vs.$Maybe\; notP$ Contradiction
   (2)$necessarily\; notP$ and$PossiblyP$ contradictory
   [Mouth formula] one must be true and the other false. If one is true, it will be false, and if one is false, it will be true. [When "must P" is true, "may not P" must be false; when "must P" is false, "may not P" must be true; and vice versa. ]
   (1)Negative proposition of modal proposition:"not" + "modal proposition", which is equivalent toremoving the previous not, and then changing the original "modal proposition" as follows:
   affirmation becomes negation, negation becomes affirmation; necessity Become possible, may become inevitable.
   (1)"Not" before the modal proposition:
   When "Not" crosses "possible, inevitable; all, some", the following interchanges are carried out:
   Impossible= necessarilynot
   necessarily notnecessarily = possiblynot
   both= somenot
   noyes = none
3. Hypothesis
   $P\to Q$ and$P\wedge ┐Q$ contradicts.
   $IfPthenQ$ and$Pand\; notQ$ are contradictory.
4. Joint selection
   (1) $P\vee Q$ and$┐P\wedge ┐Q$ is a contradiction, called$PorQ$ and$Not-Pand\; not-Q$ are contradictory.
   (2)$P\wedge Q$ and$┐P\vee ┐Q$ is a contradiction, called$PandQ$ and$Not-Por\; not-Q$ is a contradiction.
   (3)$P\forall Q$ and$(P\wedge Q)\vee (┐P\wedge ┐Q)$ is contradictory, we can get:$P\forall Q$ and$(P\wedge Q)$ Contradictions.