Peter Linz Edition 4 Exercise 1.2 Question 22 (Page No. 30)

Question

Show that the grammar $G$ =({$S$}, {$a, b$}$, S, P$), with productions

                    $S \rightarrow  SS|SSS|aSb|bSa|λ$ ,
is equivalent to the grammar 

                    $S \rightarrow SS$ ,

                    $S \rightarrow λ$ ,

                    $S \rightarrow aSb$ ,

                    $S \rightarrow bSa$ .

Answer 1

Both grammar gives equal number of a's and equal number of b's.