Xét hai mệnh đề và .
Xét hai mệnh đề và .
a) Mệnh đề đảo của mệnh đề \(A \Rightarrow B\) là: Nếu \(a,\,b \in \mathbb{R};\,a > b > 0\) thì \({a^2} > {b^2}\).
b) Mệnh đề \(A \Rightarrow B\) là mệnh đề đúng.
c) Mệnh đề đảo của mệnh đề \(A \Rightarrow B\) là mệnh đề đúng.
d) Mệnh đề \(A \Leftrightarrow B\) là mệnh đề sai.
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
a) Sai. Mệnh đề đảo của mệnh đề $A \Rightarrow B$ là $B \Rightarrow A$. Vậy mệnh đề đảo của mệnh đề $A \Rightarrow B$ là: Nếu $a^2>b^2$ thì $a, b \in \mathbb{R} ; a>b>0$.
b) Đúng. Nếu $a, b \in \mathbb{R} ; a>b>0$ thì $a^2>b^2$ là mệnh đề đúng
c) Sai. Mệnh đề đảo của mệnh đề $A \Rightarrow B$ là: Nếu $a^2>b^2$ thì
$a, b \in \mathbb{R} ; a>b>0$ là mệnh đề sai vì ví dụ $(-5)^2>(-3)^2$ nhưng $-5<-3$
d) Đúng. Vì mệnh đề $B \Rightarrow A$ sai nên mệnh đề $A \Leftrightarrow B$ là mệnh đề sai.
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