This is an undergraduate Automata. Stick to the undergraduate topics THE LECTURE NOTES I SUBMIT. FOLLOW STEPS IN THE LECTURE NOTES and only do what is said in the assignment sheet. I will attach an...

1.
From the given language the very first string which will be generated is . Hence the very first production is

Then, Case 1     
    
    ,
since production is mentioned in previous state this will produce either a string with n number of 0’s followed by n number of 1’s or n number of 1’s followed by n number of 0’s
Case 2    
        
        
Case 3    the language will also produce a string containing 0’s and 1’s at alternat position
            ,
Combining all the productions we get
        
        
2. Eliminate useless symbols
From the production string bb using
Since we can see that a string from the grammar above can’t have more than two b’s
So, we can get ‘bb’ as a string or sub-string only using as we can terminate it with , hence we can remove the production .
Therefore, the resultant grammar is:
3.
can only be removed from the grammar that do not generate string.
First, we must find nullable variables,...