Foreword:
This article is suitable for preparing for the HUEL discrete mathematics final exam. It focuses on sorting out the question types within the scope of the HUEL discrete mathematics final exam. It can not only cope with the HUEL discrete mathematics final exam, but also serve as preparatory knowledge for data structures and algorithms.
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Table of contents
Example question [Mathematical Logic Special Topic]:
Example question [Special Topic on Set Theory]:
Example question [Special Topic on Graph Theory]:
Example question [Mathematical Logic Special Topic]:
predicate formula
This question examines the equivalent expressions of contraction and expansion of quantifier scope (page 74 of the second edition of "Discrete Mathematics")
Constrained variables and free variables
Judgment of proposition
1.
2.
Quantifier scope
1.
2.
3.
Toe-in paradigm problem
Definition of toe-in paradigm:
propositional logical reasoning
Example question [Special Topic on Set Theory]:
Binary relationship
1.
2. Recommended reading: In relationships, can symmetry and antisymmetry be established at the same time? - Question from Zhihu
3.
Relationship diagram:
relational closure
There are three types of closures of relationships:
Reflexive closure: add ordered pairs to become a reflexive minimal binary relationship
Symmetric closure: add ordered pairs to become a symmetric minimal binary relationship
Transitive closure: Add ordered pairs to become the smallest binary relationship that is transitive
For example, there is the following relationship:
Reflexive closure: Add a loop to each node to become a reflexive closure
Symmetric closure: add a reverse edge between two nodes with one-way edges
Transitive closure: a→b, b→c, then a→c must be added;
Another example:
Definition of empty set
1. Just remember one thing: the empty set is a subset of any set, and the empty set is a proper subset of any non-empty set.
2. A power set is a set composed of all subsets of a set
Equivalence relations, partial order relations and compatibility relations:
Recommended reading: Set Theory—Equivalence Relationship and Partial Ordering Relationship CSDN Blogger: Baishui Baishui
Definition of equivalence relationship:
The definition of partial order relationship:
Definition of compatibility relationship:
Definition: Let R be a binary relation on the set A. If R is reflexive and symmetric , then R is said to be a consistent relation.
relation chart:
Example question [Special Topic on Graph Theory]:
Euler circuits and pathways
Euler cycle definition: a cycle in which all edges in the graph traverse all vertices once and only once;
Decision: The graph G is an undirected connected graph, and the degrees of all nodes in graph G are even numbers.
The graph G is a directed connected graph, and the in-degree of all nodes is equal to the out-degree.
Euler path definition: a path in which all edges in the graph traverse all vertices once and only once
Decision: The graph G is an undirected connected graph, and the graph G has 0 or 2 odd degree nodes.
Figure G is a directed connected graph. Except for the two endpoints, the in-degree of the other nodes = out-degree. The in-degree of one endpoint is 1 greater than the out-degree, and the in-degree of one endpoint is 1 smaller than the out-degree. It is recommended to only memorize the judgment of the Euler circuit .
What is the difference between a loop and a path?
basic definition of tree
Hasmap problem
1.
2.
Euler diagram problem
Recommended reading: Basic concepts of Euler diagrams and determination methods CSDN blogger: I am a
1. Directed graphs are generally not tested
Hamilton diagram:
Hamilton path: A path in Figure G passes through every point, then this path is a Hamilton path;
Hamilton cycle: A path in Figure G passes through every point except SS and SS only passes twice, which is a Hamilton cycle.
Definition of cut edge:
The lowest cost question:
Recommended reading: Kruskal finds the sum of weights of the minimum spanning tree CSDN blogger: Five-star General Meiyu
