Q$1[5$x$3$M $=15$M$].$ Are the following languages decidable$/$un$-$decidable? If it is decidable, prove it$.$ If not, prove by reduction using the language ATM $=\{$M$,$w$|$M$$ is a Turing Machine and $$M$$ accepts $$w$\}.$ a$)$ L$2=\{$M$$w$|$ M is Turing Machine, w is a string, and some Turing Machine M$1$ exists such that w does not belong to L$($M$)$ L$($M$1)\}$ b$)$ L$3=\{$M$|$ M is a Turing Machine that halts on all inputs and for some undecidable language B$,$ L$($M$)=$ L$($B$)\}$ c$)$ L$4=\{$M$|$ M is the Turing Machine and M is the only Turing Machine that accepts L$($M$)\}$ d$)$ L$5=\{$M$|$ M is a Turing Machine and there exist a TM M$1$ such that the encodings of M and M$1$ are not same but L$($M$)=$ L$($M$1)\}$ e$)$ L$6=\{$M$|$ M is a Turing Machine, and there exists two Turing Machines M$1$ and M$2$ such that L$($M$)$ L$($M$1)$ U L$($M$2)\}$