Exercise $2\mathrm{.}1($in Sipser text$)2.$ Give context$-$free grammars generating each of the following languages over $=\{0,1\}$:a$.\{$w : w starts and ends with the same symbol$\}$b$.\{$w : $|$w$|$ is odd$\}$c$.\{$w : $|$w$|5\}$d$.\{$w : $|$w$|>5$ or its third symbol is $0\}3.$ Give context$-$free grammars generating each of the following languages over $=\{0,1\}$:a$)\{0$n$1$m$0$n: m$,$ n $1\}$b$)\{0$n$1$n$0$m$1$m: m$,$ n $0\}$c$)\{0$n$1$m$0$m$1$n: m$,$ n $0\}4.$ Consider the language L $=\{0$n$1$m$0$k: m$,$ n$,$ k $0$ and m $=$ n or m $=$ k$\}$ over $=\{0,1\}$:a$)$ Give a context$-$free grammar generating L$.$b$)$ Show that your grammar for L is ambiguous.