Equivalent regex

Question

Consider the regex: $(a+b)^*(a+b+\epsilon)a$

Which of the following is equivalent to above?:

(a) $(a^*+b^*)^+(aa+ba)$

(b) $(\epsilon+a+b^*)^+a$

(c) $(a+b)^+(a+b+\epsilon)a$

(d) None of these

Comments

b shld be answer

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given answer ?

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what's wrong with option (a).?????

Answer 1

$$\begin{align*} &\rightarrow (a+b)^{*}(a+b+ \epsilon)a \\ &= \color{red}{(a+b)^{*}a} \\ \\ \hline \\ &\text{Option B} \\ &\rightarrow (\epsilon+a+b^{*})^{+}a \\ &=(\epsilon+a+b^{*})(\epsilon+a+b^{*})^{*}a \\ &=(a+b^{*}){\color{red}{(a+b^{*})^{*}}}a \\ &=(a+b^{*}){\color{red}{(a+b)^{*}}}a \\ &={\color{red}{(a+b^{*})(a+b)^{*}}}a \\ &={\color{blue}{(a+b)^{*}}}a \end{align*}$$

Comments

correct if wrong !

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answer given was (d) None of these. 

Using which regex law / identity you can reduce

$(a+b)^*(a+b+\epsilon)$ to $(a+b)^*$

and 

$(a+b^*)(a+b)^*$ to $(a+b)^*$

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=>  (a+b*)(a+b)*a  howdid u conveert to this =>(a+b)*a

Answer 2

Yup...
Even I feel that option b should be the right answer