Question

Let $U = R$. If $A = \{x \in R : 0 < x < 2\}$,
$B = \{x \in R : 1 < x \le 3\}$, which of the following is incorrect?

• A. $A' = \{x \in R : x \le 0$ or $x \ge 2\}$
• B. $B' = \{x \in R : x \le 1$ or $x > 3\}$
• C. $A \cup B = \{x \in R : 0 \le x \le 3\}$
• D. $A \cap B = \{x \in R : 1 < x < 2\}$

Answer 1

Answer: (C)

$A' = R - A = \{x \in R : x \le 0$ or $x \ge 2\}$

$B' = R - B = \{x \in R : x \le 1$ or $x > 3\}$
$A \cup B = \{x \in R : x \in A$ or $x \in B\}$
$ = \{x \in R : 0 < x \le 3\}$
$A \cap B = \{x \in R : x \in A$ and $x \in B\}$
$ = \{ x \in R : 1 < x < 2\}$