Question

which pair(s) of expressions are equal in value? check all that apply.$lfloor 4.9
floor$ and $lceil 3.1
ceil

$$lfloor 15.2 floor$ and $lfloor 14.8 floor$$

lfloor -6
floor$ and $lceil -6
ceil$$lceil -3.2
ceil$ and $lceil -2.6
ceil$done

Explanation:

Step1: Define floor/ceiling functions

• Floor function $\lfloor x

floor$: greatest integer ≤ $x$

• Ceiling function $\lceil x

ceil$: least integer ≥ $x$

Step2: Evaluate first pair

$\lfloor 4.9
floor = 4$, $\lceil 3.1
ceil = 4$

Step3: Evaluate second pair

$\lfloor 15.2
floor = 15$, $\lfloor 14.8
floor = 14$

Step4: Evaluate third pair

$\lfloor -6
floor = -6$, $\lceil -6
ceil = -6$

Step5: Evaluate fourth pair

$\lceil -3.2
ceil = -3$, $\lceil -2.6
ceil = -2$

Answer:

$\boldsymbol{\lfloor 4.9
floor \text{ and } \lceil 3.1
ceil}$
$\boldsymbol{\lfloor -6
floor \text{ and } \lceil -6
ceil}$