Ta có
$|2x-1| > 3$
$<-> 2x-1 > 3$ hoặc $2x-1 < -3$
$<-> x > 2$ hoặc $x < -1$
$<-> A = (-\infty, -1) \cup (2, + \infty)$
Mặt khác, lại có
$|x-2| < 4$
$<-> -4 < x-2 < 4$
$<-> -2 < x < 6$
$<-> B = (-2, 6)$
Vậy
- $A \cup B = \mathbb{R}$
- $A \cap B = (-2, -1) \cup (2, 6)$
- $A \backslash B = (-\infty, -2] \cup [6, + \infty)$
- $B \backslash A = [-1, 2]$
- $Cr(A) = [-1, 2]$
- $Cr(B) = (-\infty, -2] \cup [6, + \infty)$
- $Cr(A \cap B) = (-\infty, 2] \cup [-1, 2] \cup [6, + \infty)$.