Consider the following regular expressions over alphabet$\{a,b\}$, where the notation $(a+b)^+$ means $(a+b)(a+b)^*$:
$$r_1=(a+b)^+a(a+b)^*$$
$$r_2=(a+b)^*b(a+b)^+$$
Let $L_1$ and $L_2$ be the languages defined by $r_1$ and $r_2$, respectively. Which of the following regular expressions define $L_1\cap L_2$?
- $(a+b)^+a(a+b)^*b(a+b)^+$
- $(a+b)^*a\;b(a+b)^*$
- $(a+b)^*b(a+b)^*a(a+b)^*$
- $(a+b)^*a(a+b)^*b(a+b)^*$