Practice Question

Question

How to prove that $ (a+b)^*ab(a+b)^*+b^*a^* = (a+b)^*$

Answer 1

In L.H.S.

$\left ( a+b \right )^{*}ab\left ( a+b \right )^{*}$

It will generate all string which have 'ab' as substring.

So to prove it correct you have to accept string which does not have 'ab' as substring such as 'aa','ba','bb'.

All these are generated by b$^{*}$a$^{*}$.

Thus they are equal.