Question

Demonstrați A∩B știind că A={x∈Z | 3x-1≤5} și B={x∈Z | |x-2|≤4}.

Answer 1

[tex]A: \\ \\ 3x-1\leq 5 \Rightarrow 3x \leq 6 \Rightarrow x \leq \frac{6}{3} \Rightarrow x \leq 2 \Rightarrow A = \{2,1,0,-1,-2,-3,-4,...\} \\ \\ B: \\ \\ |x-2| \leq 4 \Rightarrow -4\leq x-2\leq 4 \big|+2 \Rightarrow -2\leq x\leq 6 \\ \Rightarrow B = \{-2,-1,0,1,2,3,4,5,6\} \\ \\ \rightarrow A \cap B = \{-2,-1,0,1,2\} [/tex]