(i) will actually include everything because we count everything which is inside P or outside Q - which technically covers the entire space (and we are in fact double counting the doughnut region).

(ii) is correct - it must be inside P AND outside Q at the same time.

(iii) is correct - we only count the region outside of the combination of all possible regions in P or Q.

(iv) is correct - we count all the regions which is outside of the intersecting region of P and Q.

(v) is correct - we count all the possible regions which are outside P or outside Q, so we do not include the inner circle. As a matter of fact, (P u Q)' is the same as P' n Q'.

(vi) is correct - we only count only the common region which is outside P and outside Q, and this must be entirely outside P. As a matter of fact, (p n Q)' is the same as P' u Q'.

(vii) is correct. P' u Q means combining the region outside P with the region inside Q, so (P' u Q)' means the region which is not described yet (the doughnut region)/

(viii) should not contain any shaded region at all. P u Q' means combining the region inside P with the region outside Q, which technically covers the entire space. So, (P u Q')' will be none of the regions since P u Q' covers every region.