Let R be a regular expression. Let S$=1$R$1$ be the regular expression denoting all strings of R with a $1$ appended toboth the beginning and the end of each string in R$.$ Delete every block of $0\text{'}$s of even length in S$.$ Prove or disprove that the resulting set is regular. $($Can this question be solved by proving it using the closure property of set difference operation?$)$