We can use the principle of inclusion-exclusion to find n(U), which states that for two sets A and B:
n(A union B) = n(A) + n(B) - n(A intersection B)
We can apply this to three sets r, s, and their complements r' and s':
n(U) = n(r union s)
= n(r) + n(s) - n(r intersection s)
= [n(r intersection s') + n(r intersection s)] + [n(s intersection r') + n(s intersection r)] - n(r intersection s)
= [(4 + n(r' intersection s)) + (n(r intersection s') + 7)] - 4
= n(r' intersection s) + n(r intersection s') + 3
= 7 + 3 + 3
= 13
Therefore, n(U) = 13.