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

Question

Which one of the following have same sense w.r.t. open and closed intervals? (A) A = [2, 3] and B = x: x ∈ R, 2 le x le 3  (B) A = [-3, 5] and B = x: x ∈ R, -3 < x le 5  (C) A = [-15, -2] and B = x: x ∈ R, -15 < x < -2  (D) A = (-1, 2 ) and B = x: x ∈ R, - 1 le x le 2

Tardigrade Admin · Accepted Answer

B = x: x ∈ R, 2 le x le 3 ⇒ x ∈ [2, 3] (using meaning of a le x le b)

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

$A = [2, 3]$ and $B = {x : x \in R, 2 \leq x \leq 3}$

$A = [- 3, 5]$ and $B = {x : x \in R, - 3 < x \leq 5}$

$A = [- 15, - 2]$ and $B = {x : x \in R, - 15 < x < - 2}$

$A = (- 1, 2)$ and $B = {x : x \in R, - 1 \leq x \leq 2}$

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

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

A=[2,3] and B={x:x∈R,2≤x≤3}

A=[−3,5] and B={x:x∈R,−3<x≤5}

A=[−15,−2] and B={x:x∈R,−15<x<−2}

A=(−1,2) and B={x:x∈R,−1≤x≤2}

B={x:x∈R,2≤x≤3} ⇒x∈[2,3] (using meaning of a≤x≤b)

$A = [2, 3]$ and $B = {x : x \in R, 2 \leq x \leq 3}$

$A = [- 3, 5]$ and $B = {x : x \in R, - 3 < x \leq 5}$

$A = [- 15, - 2]$ and $B = {x : x \in R, - 15 < x < - 2}$

$A = (- 1, 2)$ and $B = {x : x \in R, - 1 \leq x \leq 2}$

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