Q$-1.($a$)$ Let $Ai=(0,i),$ i$.$e$.,$ the set of real numbers x $,$ where $U_i=1^{}Ai{?}_i=1^{}$AiU$=\{1,2,3,4,5,6,7,8,9,10\}{i}^{th}\{3,4,5\}\{1,3,6,10\}\{2,3,4,7,8,9\}f(x)=-\frac{x}{2}$lrcornerx$0$ for every positive integer $i.$ Find $U_i=1^{}Ai$ and ${?}_i=1^{}Ai.$

$(b)$ Suppose the universal set $isU=\{1,2,3,4,5,6,7,8,9,10\}.$ Express each $of$ these sets with but strings where the $i^{th}$ bit $in$ the string $is1ifiisin$ the set and $0$ otherwise.

$(i)\{3,4,5\}$

$[3]$

$(ii)\{1,3,6,10\}$

$(iii)\{2,3,4,7,8,9\}$

$(c)$ Draw the graph for $f(x)=-\frac{x}{2}$lrcorner, where $xis$ a real number.

$[3]$