E, in turn, is the symbol "existence": it is called existential quantifier.

Full-name quantifiers: within a certain range, quantifiers that express all or all meanings are called full-name quantifiers. A proposition that contains a full-name quantifier is called a universal proposition. The negation of universal quantifier is existential quantifier.

Common quantifiers: all, any one, every one, everything, any one, etc. Symbol "?" Usually used. Say, read "to any".

Some full-name propositions may omit full-name quantifiers in text narration, such as:

(1) "The last bit is an integer of 0, which can be divisible by 5";

(2) "The distance between a point on the vertical line of a line segment and the two endpoints of this line segment is equal";

(3) "The square of a negative number is a positive number";

Are all full-name propositions.

Existential quantifiers: Quantifiers that express individual or partial meanings are called existential quantifiers. Propositions containing existential quantifiers are called special propositions. Its form is several s and p. Special propositions use existential quantifiers, such as some and several. You can also use basic, general, just some, etc.

Commonly used quantifiers of existence: one, one, at least one, one, some, etc. They are usually represented by the symbol ""and pronounced as "existence?" . For example:

(1) A special proposition can also contain multiple variables, such as existence.

(2) Some special propositions may omit existential quantifiers.

(3) The same full name proposition or proper name proposition can be expressed in different ways.

Special proposition "There is an X in M, which makes p(x) hold". Jane wrote:? x？ ∈? m，p(x).

Read: there is an x that belongs to m, which makes p(x) hold.

Extended data:

Full name proposition:

The phrases "for all" and "for any one" are usually called full-name quantifiers in logic. Are they used together? (upside down capital "a"). A is the abbreviation of any in English. A proposition containing a universal quantifier is called a universal proposition, and the negation of a universal quantifier is an existential quantifier.

For example, the proposition:

P: For any n∈Z, 2n+ 1 is an odd number.

Q: All squares are rectangles.

Are all full-name propositions.

Usually, statements containing the variable X are represented by p(x), q(x), r(x), …, and the range of the variable X is represented by M. Then, the full-name proposition "p(x) holds for any X in M" can be abbreviated as

X∈M, p(x), (If A is an element of set A, it is said that A belongs to (belongs to) set A, and it is marked as a∈A).

For any x belonging to m, P(x) holds.

The negation of full name proposition is a special name proposition.

Special proposition:

Special proposition/existential statement is an existential proposition, which contains existential quantifiers. What is the form of "some s is p" or "some s is not p" x∈M，q(x).

For example, the proposition:

P: For any n∈Z, 2n+ 1 is an odd number.

Q: All squares are rectangles.

Are all full-name propositions.

Usually, statements containing the variable X are represented by p(x), q(x), r(x), …, and the range of the variable X is represented by M. Then, the full-name proposition "p(x) holds for any X in M" can be abbreviated as

X∈M, p(x), (If A is an element of set A, it is said that A belongs to (belongs to) set A, and it is marked as a∈A).

For any x belonging to m, P(x) holds.

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