Toán Lớp 10: Giải thích đầy đủ, chi tiết: `{(- ∞;1] ∪[5;+ ∞)} ∩{(- ∞;5] ∪[9;+ ∞)}`

Question

Toán Lớp 10:  Giải thích đầy đủ, chi tiết: {(- ∞;1] ∪[5;+ ∞)} ∩{(- ∞;5] ∪[9;+ ∞)}

quynhmaithu · Answer

Giải đáp:   $ (- infty;1]  cup  {5 } cup [9;+ infty).$   Lời giải và giải thích chi tiết:   $A  cap (B  cup C)=(A  cap B)  cup (A  cap C)$   Chứng minh:   Lấy $x  in A  cap (B  cup C)$   $ Rightarrow   left { begin{array}{l} x  in A    x  in (B  cup C) end{array}  right.    Leftrightarrow    left { begin{array}{l} x  in A     left[ begin{array}{l} x  in B    x  in C end{array}  right. end{array}  right.    Leftrightarrow   left[ begin{array}{l}  left { begin{array}{l} x  in A    x  in B end{array}  right.   left { begin{array}{l} x  in A    x  in C end{array}  right. end{array}  right.    Leftrightarrow  x  in (A  cap B)  cup (A  cap C)    Rightarrow A  cap (B  cup C)  subset (A  cap B)  cup (A  cap C)(1)$    Lấy $x  in (A  cap B)  cup (A  cap C)$    $ Leftrightarrow   left[ begin{array}{l}  left { begin{array}{l} x  in A    x  in B end{array}  right.   left { begin{array}{l} x  in A    x  in C end{array}  right. end{array}  right.    Leftrightarrow    left { begin{array}{l} x  in A     left[ begin{array}{l} x  in B    x  in C end{array}  right. end{array}  right.    Leftrightarrow   left { begin{array}{l} x  in A    x  in (B  cup C) end{array}  right.    Leftrightarrow  x  in A  cap (B  cup C)    Rightarrow   (A  cap B)  cup (A  cap C)  subset A  cap (B  cup C)(2)   (1)(2) Rightarrow A  cap (B  cup C)=(A  cap B)  cup (A  cap C)$   &Aacute;p dụng:   $ Big((- infty;1]  cup [5;+ infty) Big)  cap  Big((- infty;5]  cup [9;+ infty) Big)   = Bigg( Big((- infty;1]  cup [5;+ infty) Big)  cap (- infty;5]  Bigg)  cup  Bigg( Big((- infty;1]  cup [5;+ infty) Big)  cap [9;+ infty)  Bigg)   = (- infty;1]  cup  {5 } cup [9;+ infty).$