### Problems

**"When does s* = s, where s is a compound proposition"**

The

dualof a compound proposition that contains only the logical operators AND, OR, and NOT is the compound proposition obtained by replacing each AND by OR, each OR by AND, each T by F, and each F by T. The dual ofsis denoted bys*

### Solution

Let s = P(a

_{1}, a_{2}, a_{3},…, a_{n})where a_{i}is a single proposition, and P is the relationship among a_{i}.So s* = (¬P)(a

_{1}, a_{2}, a_{3},…, a_{n})where (¬P) is the inverse relationship of Ps* = ¬(¬(¬P)(a

_{1}, a_{2}, a_{3},…, a_{n}) )double negatings* = ¬( P(¬a

_{1},¬ a_{2},¬ a_{3},…,¬ a_{n}) )

If s*= s

Then ¬P(a

_{1}, a_{2}, a_{3},…, a_{n}) = P(¬a_{1},¬ a_{2},¬ a_{3},…,¬ a_{n})

It means when we inverse every single proposition in s, if the truth value of s is also inversed, proposition s is self-dual (or s*=s)

Troi oi. May ong hoc cai gi vay ne troi. Ban Downy vua post 1 bai day lesson len AT con ban Glo thi post 1 bai doc vao ko hieu gi het do.

ReplyDeletehehe, mấy bài này về toán logic đó mà. logic mệnh đề

ReplyDelete@@@@@@@@@@@@@@@@@@

ReplyDeletehù tao hả mày. :-w :))

ReplyDeleteĐáng tiếc là không có ai sợ.

ReplyDeleteChẳng qua là viết bằng tiếng Anh nên nhìn nó lung tung chứ thật ra: toàn là trò con nít :))

nghe cái nickname là biết Shin kưxồ rồi

ReplyDelete