If A can deduce B, then A is a sufficient condition for B ... where A is a subset of B, that is, what belongs to A must belong to B, but what belongs to B does not necessarily belong to A. Specifically, if an element belongs to B but does not belong to A, then A is the proper subset of B; If what belongs to B also belongs to A, A and B are equal.

classify

life

In daily life, we often use "if, then", "if, then" and "as long as, then" to express sufficient conditions. For example:

1. If the game is tied, then the China Men's Football Team will qualify.

2. The General Staff Command: If the plane can't land, parachute directly to Wenchuan.

However, when people use these related words in their lives, they often don't consider their necessity. That is to say, when A satisfies and B is inevitable, we say that if A, then B, or as long as A, then B. This expresses the sufficiency of conditions, and we do not consider whether condition A is necessary for result B. For example:

I will write as long as I live.

Objectively speaking, if you are not satisfied with "living", you will inevitably "can't write". So "being alive" is a necessary and sufficient condition for "I want to write". But in fact, the person who said this sentence just wanted to express "I want to write" when I was alive. As for the situation that "I can't write if I'm not alive", although everyone knows it, this is not what the speaker wants to express.

Therefore, these related words in life only express the full and sufficient meaning of conditions, without considering the necessity, which is different from the strict definition of logic.

Other terms of sufficient condition: sufficient condition, sufficient condition, sufficient condition.

logic

Definition: Where there is situation A, there must be situation B; If there is no case A but not necessarily no case B, then A is a sufficient and unnecessary condition of B, which is called a sufficient condition. Immediately after "if".

Sufficient conditions come from the study of hypothetical propositions and hypothetical reasoning in logic.

A hypothetical proposition that states a sufficient condition for one thing to be another thing is called a sufficient condition hypothetical proposition. The general form of the sufficient condition hypothesis proposition is: if P, then Q. The symbol is: p→q (pronounced as "P implies Q"). For example, "an object will remain stationary or move in a straight line at a constant speed without external force" is a hypothesis with sufficient conditions.

Reasoning based on the logical properties of sufficient conditional hypothesis proposition is called sufficient conditional hypothesis reasoning. Sufficient conditional hypothesis reasoning is based on the proposition of sufficient conditional hypothesis, and draws a conclusion by affirming the antecedent or denying the latter. This reasoning structure consists of three parts, in which the major premise is the sufficient conditional hypothesis judgment, and the minor premise and conclusion are the judgments composed of the antecedents or consequences of the sufficient conditional hypothesis judgment. Lenin said: "Any science is applied logic."

Reflected in the criminal investigation, investigators found a lot of evidence, that is, physical evidence, witness and so on. As a minor premise, the thinking process of drawing a conclusion is the application of sufficient conditional hypothetical reasoning in criminal investigation. The task of investigation is to obtain the crime situation and the clues of the perpetrator through on-the-spot investigation and investigation visit. On this basis, the police should analyze and judge the case, determine the nature of the case, and put forward the investigation hypothesis, including determining the development direction of the case, guessing the scope of the perpetrator, making the direction of solving the case, then investigating and finally solving the case. In this process, from filing a case, investigation to closing the case, investigators must use logic to explore the causal relationship, especially the investigation hypothesis and reasoning that are of great significance to case detection, which all reflect the important position of sufficient conditional hypothesis reasoning in criminal investigation.

mathematics

There are propositions P and Q. If P deduces Q, then P is a sufficient condition for Q, and Q is a necessary condition for P; If p deduces q and q deduces p, then p is a necessary and sufficient condition of q, which is called the necessary and sufficient condition for short.

For example, if x=y deduces X2 = Y 2, then x=y is a sufficient condition and X2 = Y 2 is a necessary condition.

A, b pushes AB

If p deduces q, then p is a sufficient condition of q, and the necessary condition of q is as follows.

If q does not hold, then p does not hold.

Q is a necessary condition for p.

For example:

P: x= 1 Q: x^2= 1

P is a sufficient condition but not a necessary condition of q (excluding x= 1, when X =- 1 and x 2 =1).

Q is a necessary condition for P. Without X 2 = 1, there is no x= 1.

for instance

1 . a = " Rain "； B= "wetland".

2.a = "burning wood"; B= "CO2 will be produced".

In this example, A is a sufficient condition for B, to be exact, A is a sufficient and unnecessary condition for B: First, A will inevitably lead to B; Second, A is not a necessary condition for B to occur. In the example, rain will cause the ground to be wet, but it is not necessarily caused by rain, but may be caused by splashing water; Burning wood will certainly produce carbon dioxide, but carbon dioxide may be produced by burning methanol. These instructions show that A is not a necessary condition for B to occur. So A is a sufficient condition and an unnecessary condition for B, that is, a sufficient and unnecessary condition.