If A = x R: |x|

Question

If A = {$x\in\mathbb R: |x|<2$} and B = {$x\in\mathbb R: |x-2|\ge3$}; then:

Accepted Answer

$A=(-2,2)$. For B: $|x-2|\ge3 \implies x\ge5$ or $x\le-1$, so $B=(-\infty,-1]\cup[5,\infty)$.

$$A\cap B = (-2,2)\cap\big[(-\infty,-1]\cup[5,\infty)\big] = (-2,-1]$$
$$A\cup B = (-2,2)\cup(-\infty,-1]\cup[5,\infty) = (-\infty,2)\cup[5,\infty)$$
$$A-B = (-2,2)\cap(-1,5) = (-1,2)$$
$$B-A = \big[(-\infty,-1]\cup[5,\infty)\big]\cap\big[(-\infty,-2]\cup[2,\infty)\big] = (-\infty,-2]\cup[5,\infty) = \mathbb R-(-2,5)$$

Option B is correct: $B-A = \mathbb R-(-2,5)$.

Solutions · 1