Simplify : 81/2 - [ 31/4 + \ 11/4 - 1/2 ( 11/2 - 1/3 - 1/6 ) \ ]

Answer: Option A

$$\begin{array}{rl}& \text{According to the question,}\\ & \text{8}\frac{1}{2}-\left[3\frac{1}{4}+\left\{1\frac{1}{4}-\frac{1}{2}\left(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]\\ & \Rightarrow \frac{17}{2}-\left[\frac{13}{4}+\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]\\ & \Rightarrow \frac{17}{2}-\left[\frac{13}{4}+\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{9-2-1}{6}\right)\right\}\right]\\ & \Rightarrow \frac{17}{2}-\left[\frac{13}{4}+\left\{\frac{5}{4}-\frac{1}{2}\times 1\right\}\right]\\ & \Rightarrow \frac{17}{2}-\left[\frac{13}{4}+\left\{\frac{5-2}{4}\right\}\right]\\ & \Rightarrow \frac{17}{2}-\left[\frac{13}{4}+\frac{3}{4}\right]\\ & \Rightarrow \frac{17}{2}-\frac{16}{4}\\ & \Rightarrow \frac{34-16}{4}\\ & \Rightarrow \frac{9}{2}\\ & \Rightarrow 4\frac{1}{2}\end{array}$$