United Proposition and reasoning
Compound proposition is simple connectives propositional logic combination, which consists of two parts and branched propositional connectives by connective decision proposition logical properties of the composite. Depending on the nature of the link items, with complex proposition into words, disjunctive, false, negative proposition.
First, the United Proposition overview (and)
United Proposition proposition is to determine a composite of many things, circumstances exist, the joint statement supported, with connective words of two parts.
Example 1, oil brother is a student and part-time writer.
Analysis: The proposition is a joint statement. Concluded that the "oil brother is a student" and "oil Columbia is a part-time writer." In both cases exist, it is the connective "and."
United Proposition structure is: "p and q". Conjunctive word used "and" "simultaneously", "also" and so on. Mandarin Chinese coordinate compound sentences, complex sentences progressive, transitional complex sentences with words expressing general proposition.
Example 2, steep steep (Yao, straight) are easy to pack and are easy shining pollution. (Tied for complex sentence)
Example 3 yo is not only good medicine, but also doctors. (Progressive complex sentence)
Example 4, success requires effort, but it is not enough just trying to (transition complex sentence)
Example 5, the logic is the base class and elective (simple sentence)
United Proposition (and) proposition, all with the words branch is true, the proposition is true or false. Change the order with words of support does not cause joint statement Proposition change (effectiveness), but with Proposition meaning may change (meaningful).
Second, the association inference
1, factorization
It means the United Proposition true, the launch of its part of the reasoning supporting the proposition is true.
Example 1, remarks to three winter, medicine tastes bitter disease, therefore, remarks to three winter.
Analysis: the form: "if p and q true, therefore, true p." Factorization help people on the basis of a comprehensive understanding of the situation of things, focus or emphasis on a particular aspect of the case.
2, modular
Refers to the premise of the proposition is true in all, the introduction of these propositions to support the proposition with Proposition true reasoning.
Example 2, very talented at my table, my table distinctive, so my table very talented and distinctive.
Analysis: the form: "p true, true q, Hence, p-q and true." Combined help people to recognize the various aspects of things integrated into a comprehensive and complete understanding.
Disjunctive proposition and reasoning
I. Overview disjunctive proposition (or)
Disjunctive proposition is a determination by a number of things as long as there is one kind of complex proposition.
1, compatible disjunctive proposition
That concludes disjunctive proposition several possible scenarios of things that can exist simultaneously. (Disjunctive branch can exist at the same time)
Example 1, in the fourth of chicken, or king of glory.
Analysis: The structure is: "p or q (pvq)", where "v" read disjunct. Disjunctive word used "Or, perhaps ,,, may, perhaps, maybe ,,, maybe" and expressed.
Disjunctive proposition as long as there is a branch statement is true, then the proposition is true.
2, incompatible disjunctive proposition
That statement can not support the presence of (contradictory).
Example 2, with you and I love to fight, you either win or I win.
Analysis: Incompatible disjunctive word commonly used "either ,,, or not ,,, is, or ,,, or" and so on.
Second, the disjunctive reasoning
1, compatible disjunctive reasoning
Example 1 that the products are unmarketable, or because the product is poor quality, or because the saturated market demand. The survey found that, because these goods are not saturated the market demand, so the reason for poor sales of the product quality is not good.
Analysis: reasoning form: "p or q, non-p, so that, q".
Inference rules are: negative part of disjunctive branch, must certainly rest disjunctive branch; certainly part of disjunctive branch can not confirm or deny the remaining branch
2, the Incompatible Disjunction reasoning
(1) negative affirmation Incompatible Disjunction reasoning
Refers to negative disjunctive proposition incompatible part of disjunctive branch, then certainly support the rest of disjunctive reasoning.
Example 2, male or brother to buy breakfast or fourth of buying breakfast, brother Yang did not buy breakfast, it is the fourth of buying breakfast.
Analysis: in the form of "either p, or q, non-p, therefore, q".
(2) is certainly negative Incompatible Disjunction reasoning
It refers to affirmative disjunctive proposition incompatible part of disjunctive branch, and then deny the rest of the disjunctive branch reasoning.
Incompatible Disjunction reasoning rule: certainly part of disjunctive branch, we must deny the rest of the disjunctive branch; negative part of disjunctive branch, the rest will certainly support.
Hypothetical Judgment and Reasoning
First, the Hypothetical Proposition Overview
1, p to launch q, then p is a sufficient condition of q. (High number of 59, do not pass)
2, p q can not be launched, to launch q p, then p is a necessary condition of q. (Only hard, be successful, but success will not necessarily hard)
. 3, p, q can push each other between, then p q is a necessary and sufficient condition. (Even if and only if is divisible by 2. Each other)
Second, 假言 reasoning
Hypothetical reasoning is one of the prerequisites for the hypothetical proposition, and complex proposition deduction deduction according to the logic of the hypothetical proposition . Including hypothesis (condition) bluntly reasoning, transposition hypothetical reasoning, hypothetical reasoning chain of three.
1, hypothetical reasoning respect
Hypothetical reasoning is frankly one of the prerequisites for the hypothetical proposition, another premise and conclusion is categorical proposition (Proposition nature) reasoning.
(1) sufficient condition hypothetical reasoning bluntly
Sufficient condition ponens of hypothetical reasoning bluntly: refers to a hypothetical proposition is certainly a sufficient condition antecedent, then certainly later pieces.
Example 1, if the temperature is too high, then people uncomfortable, the temperature is too high, so people uncomfortable.
Analysis: The form: "If p, then q, p, therefore, q".
Denying the antecedent:
Example 2, if the oil is to learn Pa brother, and that he should have a good academic performance, poor academic performance Colombian oil, so oil is not a brother to learn Pa.
Analysis: The form: "If p, then q, non-q, therefore, non-p".
(2) necessary conditions Hypothetical reasoning bluntly
Denying the antecedent:
Example 3, only to participate in public examination to become civil servants, oil brother did not participate in the public examination, so the oil can not be a civil servant brother.
Analysis: The form: "Only p, order q, non-p, therefore, non-q".
Affirming:
Example 3, only the physical health to do the pilot, oil brother is a pilot, so the oil brother's health.
Analysis: The form: "Only p, order q, q, therefore, p".
(3) necessary and sufficient condition hypothetical reasoning bluntly.
Ponens: p if and only if q, p, thus, q.
Affirming: p if and only if q, q, therefore, p.
Denying the antecedent: p if and only if q, non-p, therefore, non-q.
Negate member: p if and only if q, non q, therefore, non-p.
2, hypothetical reasoning transposition
That is some kind of hypothetical proposition premise to derive another hypothetical proposition reasoning by transposition of its front and rear parts.
(1) sufficient condition for transposition reasoning
Form: If p, then q, therefore, only q, only p.
Example 1, if it is gold, it will be light, so that only glowing object, is gold.
(2) a necessary condition for transposition reasoning
Form: only p, only q, so if q, then p.
Example 2, only the sick, the oil brother will stop writing, so if oil brother stop writing, then he was sick.
(3) the necessary and sufficient conditions for transposition reasoning
The form: p if and only if q, So, q if and only if p.
Example 3, oil brother become information technology experts if and only if he has been deep plowing in the industry and has made remarkable achievements, so oil brother has roots in the information technology industry and has made remarkable achievements if and only if he is industry experts. (It is not a case in point)
3, hypothetical chain of reasoning
That is the premise and conclusion are hypothetical proposition, and the front and rear after a false statement of a proposition same reasoning antecedent hypothetical proposition.
(1) chain of reasoning sufficient condition
The form: p Release q, q Release r, so p Release r.
Example 1, the name is not correct, the words ring true; words ring true, then nothing will be accomplished. Therefore, the name is not correct, then nothing will be accomplished.
Example 2, if you like me, just like I am dating; if we meet, then I'll kiss your forehead. So, if I do not kiss your forehead, so that you do not like me. (After negative pieces)
(2) a necessary condition for the chain of reasoning
The form: p is pushed q, q r is launched, so the introduction of r p and p is pushed q, q r is launched, so the introduction of a non-non-r p.
Example 1, the only study hard to master knowledge; only acquire knowledge in order to have the ability to innovate. So, if you have the ability to innovate, it is hard learners. (Ponens)
Example 2, there is only water, people survive; people only survive and multiply. So, if there is no water, people do not breeding. (No antecedent)
(3) the necessary and sufficient conditions for the chain of reasoning
The form: p is the necessary and sufficient conditions of q, q is Necessary and Sufficient Conditions r, so, p is necessary and sufficient condition of r; p is the necessary and sufficient conditions of q, q is Necessary and Sufficient Conditions r, therefore, r is Sufficient conditions of p; p is the necessary and sufficient conditions of q, q is Necessary and Sufficient conditions r, therefore, necessary and sufficient conditions are not p non-r,; p is the necessary and sufficient conditions of q, q is Necessary and Sufficient conditions r, so , non-r p is the necessary and sufficient conditions.
Ah ,,, these complex proposition, is the most common life, I do not think is very important before, and later work, often eat the loss no logic, are also considered live and learn a lesson it, especially before business Some scenarios involve judgments on the proposition that can help, go to the preliminary authenticity of it.