Question

Which one of the following have same sense w.r.t. open and closed intervals?

• A. $A = [2, 3]$ and $B = \{x : x \in R, 2 \le x \le 3\}$
• B. $A = [-3, 5]$ and $B = \{x : x \in R, -3 < x \le 5\}$
• C. $A = [-15, -2]$ and $B = \{x : x \in R, -15 < x < -2\}$
• D. $A = (-1, 2 )$ and $B = \{x : x \in R, - 1 \le x \le 2\}$

Answer 1

Answer: (A)

$B = \{x : x \in R, 2 \le x \le 3\}$
$\Rightarrow x \in [2, 3]$ (using meaning of $a \le x \le b$)