ambiguous grammar (idea)

<S> --> <A>
<A> --> <A> + <A>
        | <id>
<id> --> a | b | c

A BNF grammar is considered ambiguous if it can generate a sentence using two different parse trees. In the above case, the same sentence a + b + c can be generated using these two parse trees:

<S> -+- <A> -+- <A> --- <id> --- a
     |       |  
     |       +-  +
     |       |
     |       +- <A> --- <id> --- b
     |
     +- <A> --- <id> --- c


<S> -+- <A> --- <id> --- a
     |
     +- <A> -+- <A> --- <id> --- b
             |  
             +-  +
             |
             +- <A> --- <id> --- c

A grammar that generates the same language, but is not ambiguous would be:

<S> --> <A>
<A> --> <A> + <id>
       | <id>
<id> --> a | b | c

This is chapter 3, question 8 of Concepts of Programming Languages Fourth Edition by Robert W. Sebesta