$2$ Context$-$free Languages

Problem $23.$ Prove rigorously $($by induction on an appropriate quantity$)$ that each of the following grammars generates the language $|)$:$\}\text{'}$s in $x=$#$1\text{'}$s in $\{$:$x\}.$

$($Homework $3$ Problem $3)V=\{E\}$ with production rules $E0E1E|1E0E|.$

$V=\{E\}$ with production rules $E0E1|1E0|EE||.$