Self-dual propositions


"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*


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. 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 :))

  4. nghe cái nickname là biết Shin kưxồ rồi


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