JEE MAIN - Mathematics (2022 - 25th June Evening Shift - No. 1)

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

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

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

$$A \cap B = ( - 3, - 1]$$

$$A \cup B = R - [1,3)$$

A = ($$-$$3, 1) and B = ($$-$$ $$\infty$$, $$-$$1] $$\cup$$ [3, $$\infty$$)

So, A $$-$$ B = ($$-$$1, 1)

B $$-$$ A = ($$-$$ $$\infty$$, $$-$$3] $$\cup$$ [3, $$\infty$$) = R $$-$$ ($$-$$3, 3)

A $$\cap$$ B = ($$-$$3, $$-$$1]

and A $$\cup$$ B = ($$-$$ $$\infty$$, 1) $$\cup$$ [3, $$\infty$$) = R $$-$$ [1, 3)