Question

Cho A={x\(\in\)R\(|\)1\(\le\)x\(\le\)5}

B={x\(\in\)R\(|\)4\(\le\)x\(\le\)7}

C={x\(\in\)R\(|\)2\(\le\)x<6}

a/ Hãy xác định A\(\cap\)B; A\(\cap\)C; B\(\cap\)C; A\(\cup\)C; A\(B\(\cup\)C)

b/ Gọi D={x\(\in\)R\(|\)a\(\le\)x\(\le\)b}. Hãy xác định a,b để D\(\subset\)A\(\cap\)B\(\cap\)C

Answer 1

Lời giải:

a)

\(A\cap B=\left \{ x\in\mathbb{R}|4\leq x\leq 5 \right \}\)

\(B\cap C=\left \{ x\in\mathbb{R}|4\leq x< 6 \right \}\)

\(A\cap C=\left \{ x\in\mathbb{R}|2\leq x\leq 5 \right \}\)

\(A\cup C=\left \{ x\in\mathbb{R}|1\leq x< 6 \right \}\)

\(A\setminus (B\cup C)=A\setminus \left \{ x\in\mathbb{R}|2\leq x\leq 7 \right \}=\left \{ x\in\mathbb{R}|1\leq x <2 \right \}\)

b)

Ta có: \(A\cap B\cap C=\left \{ x\in\mathbb{R}|4\leq x\leq 5 \right \}\)

Như vậy để \(D\subset A\cap B\cap C\) thì \(4\leq a,b\leq 5\) và \(a\leq b\)

Answer 2

Akai Haruma