The counter-proposition is: if B, then A;

The proposition of no is: if it is not a, it is not b;

The negative proposition is: if it is not b, it is not a.

1, no proposition in mathematics is a concept. Generally speaking, in mathematics, statements expressed by languages, symbols or formulas that can judge truth or falsehood are called propositions.

For two propositions, if the conditions and conclusions of one proposition are the negation of the conditions and conclusions of the other proposition, then the two propositions are mutually negative. If one of them is called the original proposition, then the other is called its negative proposition.

2. If the conditions and conclusions of one of the two propositions are the negation of the conclusions and conditions of the other proposition, the two propositions are called mutually negative propositions. The negation of a proposition only negates a conclusion.

If a proposition is the original proposition, the proposition that is mutually negative with it is the negative proposition of the original proposition. The original proposition and the negative proposition are equivalent propositions. If the original proposition holds, the negative proposition holds. Inverse proposition and negative proposition are equivalent propositions. If the inverse proposition holds, the negative proposition holds.

Generally speaking, in mathematics, statements that can be expressed by language, symbols or formulas and can be judged to be true or false are called propositions. For two propositions, if the conditions and conclusions of one proposition are the conclusions and conditions of another proposition, then these two propositions are called reciprocal propositions, one of which is called the original proposition and the other is called the inverse proposition of the original proposition.

Extended data

1, no proposition

(1) The negative proposition and the original proposition can be true or false.

(2) A negative proposition is equivalent to an inverse proposition, and if the inverse proposition is true, the negative proposition is true; Conversely, if the inverse proposition is false, then the negative proposition is false.

2. The inverse proposition has the property that the original proposition is true, but its inverse proposition is not necessarily true. For example:

Original proposition: If a=0, then ab=0, which is a true proposition;

Inverse proposition: If ab=0, then a=0, which is a false proposition.

3. Negative proposition

Logic holds that proposition and negative proposition are equivalent, that is, if the proposition is true, then the negative proposition is also true. The equivalence between a proposition and its negative proposition exists as an axiom, and you can neither prove it right nor prove it wrong. In fact, this thing can be regarded as an axiom. It is equivalent to the axiom "law of contradiction". Our mathematical system is based on these axioms. ?

Baidu encyclopedia-inverse proposition

Baidu Encyclopedia-Negative Proposition

Baidu Encyclopedia-No Proposition