Ullman (TOC) Edition 3 Exercise 5.1 Question 2 (Page No. 182)

Question

The following grammar generates the language of regular expression $0^{*}1(0+1)^{*}:$

$S\rightarrow A1B$
$A\rightarrow 0A|\in$
$B\rightarrow B|1B|\in$

Give leftmost and rightmost derivations of the following strings$:$

1. $00101$ 
2. $1001$ 
3. $00011$