Step-by-step answer:
U = universal set (all possible members)
P = given set
P' = complement of P, i.e. contains all members in U but NOT 1,3,5,7in P.
Thus, U=P or P'.
Here,
U={1,2,3,4,5,6,7,8}
P={1,3,5,7}
so P'={2,4,6,8}
Check: P or P' ={1,3,5,7} or {2,4,6,8} = {1,2,3,4,5,6,7,8} = U good !