Two propositions, if the condition (or hypothesis) of the first proposition is the conclusion of the second proposition, and the conclusion of the first proposition is the condition of the second proposition, then these two propositions are called reciprocal propositions; If one of the propositions is called the original proposition, then the other is called the inverse proposition of the original proposition. For example, (1) has the same angle and two straight lines are parallel; Conditions (topics): the same angle; Conclusion: Two straight lines are parallel, and its inverse propositions are as follows: (2) Two straight lines are parallel with equal isosceles angles; (3) The isosceles angles are unequal, and the two straight lines are not parallel; (4) Two straight lines are not parallel and congruent angles are not equal. Compare the similarities and differences of conditions and conclusions of propositions (1) and (3), (1) and (4). In propositions (1) and (3), the condition and conclusion of one proposition are the negation of the condition and conclusion of the other proposition, respectively. In Proposition (1) and Proposition (4), the condition and conclusion of one proposition are the negation of the conclusion and condition of the other proposition respectively. We call proposition (1) and proposition (4) mutually negative propositions; Exchange the conditions and conclusions of the original proposition, and the obtained proposition is an inverse proposition; At the same time, deny the conditions and conclusions of the original proposition, and deny whether the obtained proposition is a proposition; Exchange the conditions and conclusions of the original proposition and deny it at the same time. 2. Summary: (1) is the original proposition (2) is the inverse proposition (3) is the negative proposition (4) is the negative proposition rhetorical question: If (2) is the original proposition, then (1)(3)(4) If (3) is the original proposition, (/kloc-) If (4) is the original proposition, what are (1) (2) and (3) propositions? Key point: the meaning of "reciprocity" 3. The form of four propositions If P is the condition of the original proposition and Q is the conclusion of the original proposition (students answer, the teacher arranges and supplements), then: Original proposition: If P is the inverse proposition of Q: If P is the negative proposition of Q: If? 0? 1p？ 0? 1q negative proposition: if? 0? 1q? 0? 1p for example 1. (Textbook P, 30 cases 1) Rewrite the following propositions into the form of "If P is Q", and write their inverse propositions, negative propositions and negative propositions: (Students answer, the teacher arranges and supplements) (1) The square of negative numbers is positive; (2) The four sides of a square are equal. Analysis: The key is to find out the condition P and conclusion Q of the original proposition. Solution: (1) The original proposition can be written as follows: If a number is negative, its square is positive; Inverse proposition: if the square of a number is positive, it is negative; No proposition: if a number is not negative, its square is not positive; Inverse proposition: If the square of a number is not positive, it is not negative. Another solution: the original proposition can be written as follows: if a number is the square of a negative number, it is positive; Inverse proposition: if a number is positive, it is the square of a negative number; No proposition: if a number is not the square of a negative number, it is not a positive number; Negative proposition: If a number is not positive, it is not the square of a negative number. (2) The original proposition can be written as follows: If a quadrilateral is a square, its four sides are equal; Inverse proposition: if the four sides of a quadrilateral are equal, it is a square; No proposition: if a quadrilateral is not a square, its four sides are not equal; Negative proposition: If the four sides of a quadrilateral are not equal, it is not a square. Example 2. Let the original proposition be "when c>0, if a>b, then ac & gtBc", write its inverse proposition, negative proposition and inverse negative proposition, and judge whether they are true or false. Note: ① A proposition in the form of "If P is Q" is also a compound proposition, in which P and Q can be propositions or open sentences, for example, the proposition "If =0, then both X and Y are 0", in which P and Q are open sentences. 2 key.