Câu hỏi:
Cho tập hợp \(A = \left\{ {x\,\,|\,\,x = 3k + 2,\,\,k \in \mathbb{N},\,\,20 \le x \le 50} \right\}.\)
Tìm \(a,\,\,b\, \, c\) để \(A = \left\{ {23;\,\,26;\,\,a;\,\,29;\,\,32;\,\,b;\,\,35;\,\,41;\,\,38;\,\,c;\,\,47} \right\}.\)
- A \(\left( {a;b;c} \right) = \left\{ {\left( {20;44;50} \right)\,\,;\,\,\left( {20;50;44} \right)\,\,;\,\,\left( {50;20;44} \right)\,\,;\,\,\left( {50;44;20} \right)\,\,;\,\,\left( {44;50;20} \right)\,\,;\,\,\left( {44;20;50} \right)} \right\}\)
- B \(\left( {a;b;c} \right) = \left\{ {\left( {24;42;51} \right)\,\,;\,\,\left( {24;51;42} \right)\,\,;\,\,\left( {51;24;42} \right)\,\,;\,\,\left( {51;42;24} \right)\,\,;\,\,\left( {42;51;24} \right)\,\,;\,\,\left( {42;24;51} \right)} \right\}\)
- C \(\left( {a;b;c} \right) = \left\{ {\left( {25;40;56} \right)\,\,;\,\,\left( {25;56;40} \right)\,\,;\,\,\left( {56;25;40} \right)\,\,;\,\,\left( {56;40;25} \right)\,\,;\,\,\left( {40;56;25} \right)\,\,;\,\,\left( {40;25;56} \right)} \right\}\)
- D \(\left( {a;b;c} \right) = \left\{ {\left( {28;46;52} \right)\,\,;\,\,\left( {28;52;46} \right)\,\,;\,\,\left( {52;28;46} \right)\,\,;\,\,\left( {52;46;28} \right)\,\,;\,\,\left( {46;52;28} \right)\,\,;\,\,\left( {46;28;52} \right)} \right\}\)
Phương pháp giải:
Liệt kê các phần tử của tập hợp \(A\) rồi xác định các giá trị \(a,\,\,b,\,\,c.\)
Lời giải chi tiết:
Ta có: \(A = \left\{ {x\,\,|\,\,x = 3k + 2,\,\,k \in \mathbb{N},\,\,20 \le x \le 50} \right\} = \left\{ {20;\,\,23;\,\,26;\,\,29;\,\,32;\,\,35;\,\,38;\,\,41;\,\,44;\,\,47;\,\,50} \right\}.\)
Để \(A = \left\{ {23;\,\,26;\,\,a;\,\,29;\,\,32;\,\,b;\,\,35;\,\,41;\,\,38;\,\,c;\,\,47} \right\}.\)
\( \Rightarrow a = 20,\,\,b = 44,\,\,\,c = 50\) hoặc \(a = 20,\,\,b = 50,\,\,c = 44\) hoặc \(a = 50,\,\,b = 20,\,\,c = 44\) hoặc \(a = 50,\,\,b = 44,\,\,c = 20\) hoặc \(a = 44,\,\,b = 50,\,\,c = 20\) hoặc \(a = 44,\,\,b = b = 20,\,\,c = 50.\)
Chọn A.
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