Let $=\{a,b\}.$ As the following example shows, for each regular expression, write the formal English

description of the set described by the regular expression. $20$ points

Example:

$(01{)}^{*}00(01{)}^{*}11(01{)}^{*}$

Answer: where $x$ contains substring $00$ and $y$ contains substring $11\}$

a$)a^{*}b{a}^{*}b{a}^{*}{b}^{*}a{b}^{*}a{b}^{*}$

b$)a^{*}(b{a}^{*}b{a}^{*}{)}^{*}$

c$)(ab{)}^{*}{a}^{*}b{a}^{*}b{a}^{*}$

d$)(ab{)}^{*}(bba$baa$)aaa$