$($a$)$ In formaldehyde $($methanal$)$ determine the irreducible representation which each of the following AOs on the carbon transforms as: the $2$s$,$ the three $2$p AOs and the five $3$d$.$ Repeat the process forthe corresponding AOs on the oxygen.

$($b$)$ The species $[$PtCl$2$Br$2]$

$2$ has square planar coordination about the platinum atom with the two

chlorine ligands being placed at opposite corners of the square. Determine the point group and

hence the irreducible representation for each of the five $5$d AOs on the platinum.