$($d$)(3$ points$)$ We would like to show that the language

is a Turing machine that accepts all strings of length strictly le than $k$ is Turing$-$recognizable.

i$.$ Let's think of the case when $k=2,($:$M,2$:$)in{A}^{AA}$ when $M$ accepts all string length less than $2$ so when $M$ accepts strings: $lon,0,1$ What strings should $M$ accept so that $($:$M,3$:$)in{A}^{AA}$