If \( G=U(32)=\{1,3,5,7,9, \ldots .31\} \) and \( H=\{1,15\} \).
a. What is \( |\mathrm{G}| \) and \( |\mathrm{H}| \) ?
b. Determine the order of the distinct right *left) cosets.
c. Identify the distinct right cosets of \( \mathrm{H} \).
d. Determine whether \( \mathrm{H} \) is normal in \( \mathrm{G} \). Explain.