Knowledge points of noun quantifiers and existential quantifiers in college entrance examination mathematics (1)
1, full-name quantifier and full-name proposition:
① Full name quantifier: phrase? Everyone's? ,? Yeah, arbitrary? In the statement, it means all or all. In logic, it is usually called a full-name quantifier, and symbols?
? Express delivery;
② Full name proposition: A proposition with full name quantifiers is called a full name proposition.
(3) The format of the full name proposition:? Is p(x) true for any x in m? Remember this proposition? x？ M, p(x), pronunciation? Does p(x) hold for any x belonging to m? .
2. There are quantifiers and special propositions;
① Existential quantifier: phrase? Really? ,? At least one? To express the meaning of an individual or part in a sentence is usually called an existential quantifier in logic, which uses symbols?
? Express delivery.
Special proposition: the proposition containing existential quantifiers is called special proposition;
③? There is a x0 in m, which makes p(x0) hold? Remember this proposition? x0？ M, p(x0), pronounced as? There is an x0 belonging to m, which makes p(x0) hold? .
3. The negation of the full name proposition:
Generally speaking, for the negation of the full-name proposition containing quantifiers, there are the following conclusions:
Full name proposition p:
This is not a proposition.
4, the negation of special proposition:
Generally speaking, for the negation of special propositions containing quantifiers, there are the following conclusions:
Special proposition p:
, its negative proposition
Knowledge points of noun quantifiers and existential quantifiers in college entrance examination mathematics (2)
Emphasis and difficulty: through rich examples in life and mathematics, understand the meaningful usage of full-name quantifiers and existential quantifiers; Can accurately say the meaning of quantifiers and existential quantifiers.
Requirements: ① Understand the meanings of universal quantifiers and existential quantifiers.
(2) Can correctly deny the proposition containing quantifiers.
Classic example: judge whether the following proposition is a full name proposition or an existence proposition.
(1) The distance between the point on the vertical line of the line segment and the two endpoints of the line segment is equal; (2) The square of a negative number is a positive number;
(3) Some triangles are not isosceles triangles; (4) Some diamonds are square.
Classroom exercises:
1. For the proposition? The square of any real number is nonnegative? , the following statement is correct ()
A. This is a full-name proposition B, which is an existential proposition.
C. is a false proposition D. is it? What if p is q? Formal proposition
2. Proposition? Are the images of the original function and the inverse function symmetrical about y=x? The negation of is ()
The images of the original function and the inverse function are symmetric about y =-X.
The image asymmetry of b primitive function about y = X and inverse function.
C The image with primitive function and inverse function is not symmetric about y = x.
The images of d primitive function and inverse function are symmetric about y = X.
3. The following full name proposition, the correct proposition is ()
A. all prime numbers are odd B.
，(x- 1)2 & gt； 0
C.
，x+？ Two dimensions.
，sinx+？ 2
4. The following existential proposition, false proposition is ()
A.
,
B. at least one x? Z.x is divisible by 2 and 3.
C. there are two intersecting planes perpendicular to the same straight line D.
Is an irrational number }.x2 is a rational number.
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