Take a look at the grammar below and solve the following problems.

$SSS|0S1|1S0$

$S$

$($a$)$ Give a leftmost derivation for the string $011010.$

$($b$)$ Sketch the parse tree corresponding to the derivation you gave in $($a$).$

$($c$)$ Demonstrate that the given grammar is ambiguous by showing three more parse trees $($apart from the one

you already found in $($b$))$ for the same string

$($d$)$ Find a string $w$ of length six such that $w$ has exactly one parse tree in the grammar above.

$($e$)$ Desgin an unambiguous Context Free Grammar for the language represented by the given ambiguous

grammar.