离散数学--关键leeds笔记

WEEK 9 : partal oreder and total order and compose function 

 

 

 

 

WEEK 8: Equivalence Relations and Functions 

WEEK 7 : inductive 推论

WEEK 6:

谓词和前面的联系

WEEK 5: 是各种证明

theorem : something known to be true.

lemma : usually a small key step towards justifying something

proposition Often just something known to be true
(like a theorem or a lemma)

 

corollary follows quickly from something earlier
conjecture could be true, but there is no known proof
axiom assumed and used as basis for further deductions

proof时 要和写python 一样注意缩进 

 

 

WEEK 4:

 任意是推 -> 存在是^

WEEK 3 :

Tautology , Contradiction,Contingency, Satisfiability 

logical imply : a->b 是永真的, 永远不可能出现 TF

have the many laws about the Equivalence

WEEK 2 :

but and -> ^ 

or directly use the v

 WEEK 1 : 

补充 superset 概念. proper 是真的意思

理解这个符号的时候, 直接利用>= 就行,谁大放那边

一些集合符号

 

 

Types of Proof
direct proof
Prove α → β by:assume α is true use this to derive β.
indirect proof
a proof that is not direct;
includes:
proof by contraposition
proof by contradiction

proof by contraposition
prove α → β by: prove ¬β → ¬α
proof by contradiction
prove α by: assume ¬α show this is impossible

 

 

要写原因: 

 

∣∣∣​{x⊆A:∣x∣=2}∣∣∣​=20(0−1)​.

 

Use $$C^2_n$$ to express $$|\{x⊆A:∣x∣=2\}|= \frac{n(n−1)}{2}$$
$$C^2_n =\frac{1}{} $$