gateforum notebook

Question

which of the  following is false?

1) every CFG  with useless symbols can be converted into an equivalent grammar with no useless symbols

2) every CFG  with ε - production may be converted into an equivalent grammar  without ε - productions that generates the same language.

Comments

The second one will be false.

Lets consider the following context free Grammar

S->AB/a

A->aAB/ε

B->b/ε

Lets try to remove ε

S->AB/A/B/a/ε

A->aAB/aA/aB/a

B->b

We can't eliminate ε since the start symbol produces ε in other words language represented by the grammar contains ε.

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ok i got it thank u