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Mệnh đề kéo theo

Mệnh đề “Nếu P thì Q” được gọi là mệnh đề kéo theo. Kí hiệu là (P Rightarrow Q).

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1. Lý thuyết

+ Định nghĩa: Cho hai mệnh đề \(P\) và \(Q\). Mệnh đề “Nếu P thì Q” được gọi là mệnh đề kéo theo. Kí hiệu là \(P \Rightarrow Q\).

+ Ví dụ: P: “\(2a - 5 > 0\)”, Q: “\(a > 3\)”

Mệnh đề \(P \Rightarrow Q\) là: “Nếu \(2a - 5 > 0\) thì \(a > 3\)”Mệnh đề \(Q \Rightarrow P\) là: “Nếu \(a > 3\) thì \(2a - 5 > 0\)”

+ Tính đúng - sai của mệnh đề \(P \Rightarrow Q\)

Mệnh đề \(P \Rightarrow Q\) chỉ sai khi P đúng và Q sai.

+ Phát biểu mệnh đề \(P \Rightarrow Q\):

Tùy theo nội dung, ta có thể phát biểu là “P kéo theo Q”, “Từ P suy ra Q”, “Vì P nên Q”
Khi mệnh đề \(P \Rightarrow Q\) đúng, nó là một định lí. Ta nói:

P là giả thiết, Q là kết luận của định lí P là điều kiện đủ để có Q Q là điều kiện cần để có P

2. Ví dụ minh họa

+ Mệnh đề kéo theo

“Nếu ABC là tam giác đều thì nó là tam giác cân”“Nếu \({a^2} - 4 = 0\) thì \(a = 2\)”

+ Tính đúng – sai

“Nếu ABC là tam giác đều thì nó là tam giác cân” đúng.“Nếu \({a^2} - 4 = 0\) thì \(a = 2\)” sai vì \(a = - 2\) thì ta cũng có \({a^2} - 4 = 0\).

+ Phát biểu mệnh đề

“ABC là tam giác đều kéo theo nó là tam giác cân” Hoặc “Vì ABC là tam giác đều nên nó là tam giác cân”.

“ABC là tam giác đều là điều kiện đủﷺ để nó là tam giác cân” hoặc “ABC là tam giác cân là điều kiện cần để nó là tam giác đều”

“Từ \({a^2} - 4 = 0\) suy ra \(a = 2\)” hoặc “\({a^2} - 4 = 0\) kéo theo \(a = 2\)”

Chia sẻ

Bình luận

Bình chọn:

4.9 trên 7 phiếu

💛 Mệnh đề đảo. Mệnh đề tương đương Mệnh đề (Q Rightarrow P)được gọi là mệnh đề đảo của mệnh đề (P Rightarrow Q). Nếu cả hai mệnh đề (P Rightarrow Q) và (Q Rightarrow P) đều đúng thì ta nói P và Q là hai mệnh đề tương đương. Kí hiệu là (P Leftrightarrow Q).
💙 Mệnh đề chứa kí hiệu Với mọi, Tồn tại + Kí hiệu (forall ) đọc là “với mọi” + Kí hiệu (exists ) đọc là “tồn tại”
💟 Mệnh để phủ định Mệnh đề “Không phải P” được gọi là mệnh đề phủ định của mệnh đề (P). Kí hiệu là (overline P ).
♐ Mệnh đề chứa biến Một khẳng định nhưng không là mệnh đề, nhưng nếu cho một giá trị cụ thể thì câu đó cho ta một mệnh đề. Những câu như vậy được gọi là mệnh đề chứa biến.
Mệnh đề Mệnh đề logic (hay mệnh đề) là một khẳng định đúng hoặc sai. Mệnh đề toán học là những mệnh đề liên quan đến toán học.

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