Let A = { x in R : | x + 1 |

Question

(B) First,solve for set $A$: $|x + 1| < 2 \implies -2 < x + 1 < 2 \implies -3 < x < 1$. So,$A = (-3, 1)$.Next,solve for set $B$: $|x - 1| \geq 2 \impl

Vedclass · Accepted Answer

$B - A = R - (-3, 1)$

Vedclass · Answer

(B) First,solve for set $A$: $|x + 1| Next,solve for set $B$: $|x - 1| \geq 2 \implies x - 1 \leq -2$ or $x - 1 \geq 2 \implies x \leq -1$ or $x \geq 3$. So,$B = (-\infty, -1] \cup [3, \infty)$.Now,evaluate the options:$A - B = (-3, 1) - ((-\infty, -1] \cup [3, \infty)) = (-1, 1)$. This is true.$B - A = ((-\infty, -1] \cup [3, \infty)) - (-3, 1) = (-\infty, -3] \cup [3, \infty) = R - (-3, 3)$. The statement $B - A = R - (-3, 1)$ is false.$A \cap B = (-3, 1) \cap ((-\infty, -1] \cup [3, \infty)) = (-3, -1]$. This is true.$A \cup B = (-3, 1) \cup (-\infty, -1] \cup [3, \infty) = (-\infty, 1) \cup [3, \infty) = R - [1, 3)$. This is true.Therefore,the statement that is $NOT$ true is option $B$.

Let $A = \{ x \in R : | x + 1 | < 2 \}$ and $B = \{ x \in R : | x - 1 | \geq 2 \}$. Then which one of the following statements is $NOT$ true?

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