Intervall

Bestätigen Sie die folgenden Bezeichnungen, die richtige Schreibweise der Intervallen bezeichnet. a. \( [a,\infty[==(a,\infty) \) [blank_start]f[blank_end] b. \( ]\pi,\infty[==[a,\infty) \) [blank_start]f[blank_end] c. \( ]a,\pi[==(a,\pi] \) [blank_start]r[blank_end]

Schreiben Sie die Intervalle in der Mengenschreibweise a. \( ]2,5]\ := \{x\in\mathbb{R}\ |\ 2 \)[blank_start]a[blank_end]\( x \)[blank_start]a[blank_end]\( 5\} \) b. \( [-1,7]\ := \{x\in\mathbb{R}\ |\ -1 \)[blank_start]a[blank_end]\( x \)[blank_start]a[blank_end]\( 7\} \) c. \( ]-3,3[\ := \{x\in\mathbb{R}\ |\ -3 \)[blank_start]a[blank_end]\( x \)[blank_start]a[blank_end]\( 3\} \) Hinweis : Ergänzen Sie die Lücke mit 1. < 2. \(\le\)

Vereinfachen Sie: a. \( ]2,5]\ \backslash\ ]3,5] \) = [blank_start]a[blank_end][blank_start]b[blank_end],[blank_start]c[blank_end][blank_start]d[blank_end] b. \( ]0,7]\ \backslash\ [0,3[ \) = [blank_start]a[blank_end][blank_start]b[blank_end],[blank_start]c[blank_end][blank_start]d[blank_end] c. \( ]-10,2]\ \cup\ [0,3[ \) = [blank_start]a[blank_end][blank_start]b[blank_end],[blank_start]c[blank_end][blank_start]d[blank_end] d. \( ]2,\infty[ \cap [-1,3[ \) = [blank_start]a[blank_end][blank_start]b[blank_end],[blank_start]c[blank_end][blank_start]d[blank_end]

Gegeben seien \(A\ := \{x\in\mathbb{R}\ |\ x<10\} \), \(B\ := \{x\in\mathbb{R}\ |\ x<5\} \), \(C\ := \{x\in\mathbb{R}\ |\ -2<x\} \), \(D\ := \{x\in\mathbb{R}\ |\ 0<x\} \), \(E\ := \{x\in\mathbb{R}\ |\ -3<x\le5\} \) und \(F\ := \{x\in\mathbb{R}\ |\ 2<x\le4\} \) Dann gilt : \(]-2,10[\ =\ (\)[blank_start]A[blank_end]\( \cup E)\)[blank_start]\cap[blank_end]\( C\ =\ A \cap \)[blank_start]C[blank_end] \((-\infty,\infty)\ =\ D \)[blank_start]\cup[blank_end] [blank_start]B[blank_end] \(\{1,2\}\ =\ (\)[blank_start]D[blank_end]\( \cap B) \)[blank_start]\backslash[blank_end]\( F \)