A coder in the BADIDEA ${?}^1$ programming language reads the technical manual and discovers

that both logical or $(11)$ as well as logical not $(1)$ execute much faster than logical and $($&&$).$

With this in mind, the coder decides to remove all logical ands for their code, replacing

them with the other logical operators. Rewrite each of the following conditions accordingly,

assuming that all function calls return a boolean value:

$($a&&$,x>999$

$($b$)f(x)$ & $lg(x)$

$($c$)$ If $(x)$ II be $($x$)$ && careful $($x$)$