First, the negative part is different.
1, non-P (propositional negation) only negates the conclusion.
2. The negative proposition of P has neither conditions nor conclusions, and all qualifiers, conditions and conclusions need to be denied.
3. Give an example.
Original proposition P: Two straight lines are parallel and have the same angle.
Non-P: Two straight lines are parallel and the same angle is not equal.
P no proposition: two straight lines are not parallel and the same angle is not equal.
Second, the relationship with the original proposition is different.
1, non-p: A proposition is completely opposite to its negative form. There is one and only one between the two.
Reduction to absurdity is often used in mathematics. To prove a proposition, we only need to prove that its negative form is not valid.
If P is a false proposition, then non-P must be a true proposition. If p is true, then non-p must be false.
2. The negative proposition of P: For the negative proposition, whether it holds or not is not directly related to whether the original proposition holds or not. There is no correspondence between its authenticity and the original proposition.
3. Give an example.
Original proposition P: If all three angles of a triangle are acute, then the triangle is an acute triangle. (correct)
Non-P: There is a triangle whose three angles are acute. This triangle is not an acute triangle. (error)
P has no proposition: there is a triangle, and all three angles are not acute. This triangle is not an acute triangle. (correct)
Third, the definition is different.
1, non-p: the negation of a proposition is the negation of the truth value of this proposition. The negation of the proposition is contrary to the truth of the original proposition.
2. No proposition of P: If the condition and conclusion of one of the two propositions are the negation of the condition and conclusion of the other proposition, then the two propositions are called mutually negative propositions.
Baidu encyclopedia-negation of proposition