Question

Daca A={x apartine Z||1-x|< sau egal 1} atunci A={....}

Answer 1

$|1-x | \leq 1 \Leftrightarrow -1 \leq 1-x \leq 1. \\ \\ -1 \leq 1-x \leq 1~~~~~~~|-1 \\ \\ -2 \leq -x \leq 0~~~~~~~~~~|:(-1) \\ \\ 2 \geq x \geq 0,~x \in Z \Rightarrow x \in \{0,1,2\}. \\ \\ Deci~A= \{0,1,2\}.$