Let $=\{$a$,$ b$,$ c$\}.$ For each of the following, construct a context free grammar G such that $($a$)$ L$($G$)=\{$a ib jc k in $|$ i$,$ j$,$ k in N$,$ j $=$ i $+$ k$\}($b$)$ L$($G$)=\{$a ib jc k in $|$ i$,$ j$,$ k in N$,$ i $=$ j or i $=$ k$\}($c$)$ L$($G$)=\{$a ib jc k in $|$ i$,$ j$,$ k in N$,$ i $<$ j or i $>$ k$\}($d$)$ L$($G$)=\{$a ib j in $|$ i$,$ j in N$,$ i $$ j $2$i$\}$