Say I am given that $\displaystyle w^r$ means the string is spelled backwards. Ex:

$\displaystyle (hello)^R$ = olleh

The definition is:

1. w is a string of length 0 then w^R = empty set

2. w = ua, where $\displaystyle a \in \Sigma $ and $\displaystyle u \in \Sigma ^ \ast $ , is a string of length n+1>0 then $\displaystyle w^r = au^R$

prove the following:

a. $\displaystyle (xy)^R = y^Rx^R$