### Problems

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

The dual of 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 of s is denoted by s*

### Solution

Let s = P(a1, a2, a3,…, an) where ai is a single proposition, and P is the relationship among ai.

So s* = (¬P)(a1, a2, a3,…, an) where (¬P) is the inverse relationship of P

s* = ¬(¬(¬P)(a1, a2, a3,…, an) ) double negating

s* = ¬( P(¬a1,¬ a2,¬ a3,…,¬ an) )

If s*= s

Then ¬P(a1, a2, a3,…, an) = P(¬a1,¬ a2,¬ a3,…,¬ an)

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)

1. 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.

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

3. @@@@@@@@@@@@@@@@@@

4. hù tao hả mày. :-w :))

5. Đáng tiếc là không có ai sợ.
Chẳng qua là viết bằng tiếng Anh nên nhìn nó lung tung chứ thật ra: toàn là trò con nít :))

6. nghe cái nickname là biết Shin kưxồ rồi

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