What is a necessary but not sufficient condition? Is there a difference between a necessary conditio

Necessary not sufficient condition, if there is a thing case B, then there must be a thing case A; If there is a situation of things A and not necessarily a situation of things B, A is a necessary and insufficient condition of B.

If A can push out 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, and what belongs to b does not necessarily belong to a, specifically if the existing elements belong to b and do not belong to a, then a is a true subset of b; If what belongs to B also belongs to A, then A is equal to B.

Suppose A is the condition and B is the conclusion:

1) B can be deduced from A, and A can be deduced from B, then A is a sufficient and necessary condition of B (A=B).

2) B can be deduced from A, and A cannot be deduced from B, then A is a sufficient and unnecessary condition for B (A ≠B).

3) B cannot be deduced from A, and A can be deduced from B, then A is a necessary and insufficient condition for B (B ≠A).

4) If B cannot be deduced from A, and A cannot be deduced from B, then A is neither sufficient nor necessary for B (A ≠B and B ≠A).

In general, if p is known to push out q, then we say that p is a sufficient condition for q and q is a necessary condition for p.

In general, if there is both P pushing out Q and Q pushing out P, then P is both a sufficient condition for Q and a necessary condition for Q, and we say that P is a sufficient and necessary condition for Q, referred to as a sufficient and necessary condition.

For example, "x is a multiple of 6" is a sufficient but not necessary condition for "x is a multiple of 2".

x is a multiple of 2" is a necessary but not sufficient condition for "x is a multiple of 6".

x is both a multiple of 2 and a multiple of 3" is a sufficient and necessary condition for "x is a multiple of 6".

A is a necessary but not sufficient condition for B.

Conclusion A can be deduced on the condition of B, but conclusion B cannot be deduced on the condition of A

Condition P cannot lead to conclusion Q, whereas conclusion Q can lead to condition P

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There is a difference.

Necessary condition: If there is no thing case a, then there must be no thing case B, that is to say, if there is thing case B, then there must be thing case a, then A is a necessary condition of B.

From a logical point of view, B can deduce A, and A is a necessary condition for B, which is equivalent to B is a sufficient condition for A.

Necessary but not sufficient conditions:

It is one of the terms of logic, from a can not deduce b, from b can deduce a, then a is a necessary and insufficient condition of b.

Suppose A is the condition and B is the conclusion:

1) B can be deduced from A, and A can be deduced from B, then A is a sufficient and necessary condition of B (A=B).

2) B can be deduced from A, and A cannot be deduced from B, then A is a sufficient and unnecessary condition for B (A ≠B).

3) B cannot be deduced from A, and A can be deduced from B, then A is a necessary and insufficient condition for B (B ≠A).

4) If B cannot be deduced from A, and A cannot be deduced from B, then A is neither sufficient nor necessary for B (A ≠B and B ≠A).

Necessary: It is a necessary condition for P to be able to launch.

Necessary and insufficient condition: P can push Q, but the fact that Q cannot be deduced is a necessary and insufficient condition for P.

Necessary conditions: the conclusion can be reversed, but it is uncertain whether the condition can lead to the conclusion;

Necessary but insufficient condition: The conclusion can be reversed from the condition, but the condition cannot lead to the conclusion.

A sufficient condition means that this condition can lead to a certain conclusion, but this condition is not necessary and there are other conditions that can satisfy this conclusion; A necessary condition means that a conclusion must have this condition, and if it is not, it will not work.

Example: Conclusion 1: a*b=0, Conclusion 2: a=0

Conclusion 1 is the necessary (non-sufficient) condition for conclusion 2, while conclusion 2 is a sufficient (non-essential) condition for conclusion 1.

And when two conclusions can be deduced from each other, then it is called a sufficient and necessary condition (i.e., sufficient and necessary condition).

For example, conclusion 3: a*b=0, conclusion 4: a=0 or b=0 or a=b=0, then conclusion 3 and conclusion 4 are mutually sufficient and necessary conditions.

If there is a situation A of things boring, then there must be a situation of things B. If there is a situation of things B and there is not necessarily a situation of things a, a is a sufficient and unnecessary condition of b, that is, a sufficient and unnecessary condition.

A is a sufficient or unnecessary condition for B B is a necessary or insufficient condition for A.

Detailed: Suppose A is the condition and B is the conclusion.

1) B can be pushed out from Qi Chenzhi from A, and A can be pushed out from B, then A is a sufficient and necessary condition for B.

a=b)。2) B can be deduced from A, and A cannot be deduced from B, then A is a sufficient and unnecessary condition for B (A ≠B).

3) B cannot be deduced from A, and A can be deduced from B, then A is the hypertonic necessary and insufficient condition of B (B A).

4) If B cannot be deduced from A, and A cannot be deduced from B, then A is neither sufficient nor necessary for B (A ≠B and B ≠A).

The necessary and insufficient condition means: if there is a thing case B, then there must be a thing case A; If there is a situation of things A and not necessarily a situation of things B, A is a necessary and insufficient condition of B. The necessary condition is the inverse process of the sufficient condition.

First, the conditions are different.

1. Necessary and insufficient conditions.

If there is a thing case B, then there must be a thing case A; If there is a situation of things A and not necessarily a situation of things B, A is a necessary and insufficient condition of B.

2. Sufficient and unnecessary conditions.

If there is a case of things, then there must be a case of thingsb of things; If there is a situation of things B and there is not necessarily a situation of things a, a is a sufficient and unnecessary condition of b, that is, a sufficient and unnecessary condition.

Second, the characteristics are different.

1. Necessary but not sufficient condition: Condition B is deduced from condition a, then b is a necessary condition of a.

2. Sufficient and unnecessary conditions: the two conditions can be deduced from each other.