MindMap Gallery Sets and Common Logic Languages
Mathematics Sets and Common Logic Language in the First Year of High School brings together some determinable and different objects. It is said that these objects form a set. Each object forming the set is a set element.
Edited at 2024-02-12 17:10:55This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
This is a mind map about Deep Analysis of Character Relationships in Zootopia 2, Main content: 1、 Multi-layer network of relationships: interweaving of main lines, branch lines, and hidden interactions, 2、 Motivation for Character Behavior: Active Promoter and Hidden Intendant, 3、 Key points of interaction: logic of conflict, collaboration, and covert support, 4、 Fun Easter eggs: metaphorical details hidden in interactions.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
This is a mind map about Deep Analysis of Character Relationships in Zootopia 2, Main content: 1、 Multi-layer network of relationships: interweaving of main lines, branch lines, and hidden interactions, 2、 Motivation for Character Behavior: Active Promoter and Hidden Intendant, 3、 Key points of interaction: logic of conflict, collaboration, and covert support, 4、 Fun Easter eggs: metaphorical details hidden in interactions.
Sets and Common Logic Languages
gather
Sets and their representation
gather
definition
By bringing together some determinable, different objects, it is said that these objects form a set, and each object that makes up the set is a set element.
certainty
Mutuality
disorder
Contains a finite number of elements
finite set
Contains unlimited elements
infinite set
display method
gather
Usually represented by English capital letters A, B, C...
element
Usually represented by English lowercase letters a, b, c...
If a is an element in A, it is written as a∈A
Several common number sets
set of natural numbers
N
set of positive integers
N*
set of integers
Z
set of rational numbers
Q
set of real numbers
R
Enumeration method
List the elements in the set one by one
descriptive method
Generally, if any element A can be represented by its characteristic property p(x) as ﹛x丨p(x)﹜
Interval and its representation
if a<b
The set ﹛x丨a≤x≤b﹜can be abbreviated as [a, b]
The set ﹛x丨a<x<b﹜ can be abbreviated as (a, b)
Basic relations of sets
Subset
If any element in set A is an element in set B, then set A is called a subset of set B.
Denoted as A⊆B
The empty set is a subset of any set
True subset
If a set A is a subset of a set B, and at least one element in B does not belong to A, then the set A is called a proper subset of the set B.
Denoted as A⫋B
Basic operations on sets
intersection
Given two sets A and B, the set consisting of all elements belonging to both A and B is called the intersection of A and B.
Denoted as A∩B
union
Given two sets A and B, the set consisting of all elements of these two sets is called the union of A and B.
Denoted as A∪B
Complement
If the sets to be studied are all subsets of a given set, then the given set is called the complete set, usually represented by U.
If a set A is a subset of the complete set U, then the set consisting of all elements in U that do not belong to A is called the complement of A in U
denoted as CuA
Commonly used logic languages
propositions and quantifiers
proposition
Statements and sentences that can be judged as true or false, such as "opposite angles are equal", are propositions.
and
A statement judged to be true is called a true proposition
Statements judged to be false are called false propositions
quantifier
The general "any" and "all" in a statement express the entirety of the stated affairs, and are called universal quantifiers.
Symbol: ∀
"Existence" and "have" represent the individual or part of the stated matter in the statement, which are called existential quantifiers
Symbol: ∃
Negation of universal quantifier propositions and existential quantifier propositions
negation of proposition
By negating the proposition p, we get a new proposition, denoted as ┐p
Negation of universal quantifier propositions and existential quantifier propositions
The negation of existential quantifier proposition is universal quantifier proposition
The negation of the universal quantifier proposition is the existential quantifier proposition
sufficient conditions, necessary conditions
sufficient condition, necessary condition
When p ⇒ q, it is said that p is a sufficient condition for q and q is a necessary condition for p.
Necessary and Sufficient Condition
If p⇒q, q⇒p, then p is said to be an essential condition of q