What does the shaded region represent in the figure given below ?

Options

A. `(PuuQ)-(PnnQ)`
B. `Pnn(QnnR)`
C. `(PnnQ)nn(PnnR)`
D. `(PnnQ)uu(PnnR)`

Answer

D

Explanation

The shaded region represents `(PnnQ)uu(PnnR)`.
Let the intersecting sets P, Q, R divide it into 7 regions marked, a to g as shown below.

The shaded part contains regions b, c, and d.
(a) `(PuuQ)-(PnnQ)-=` regions a, b, c, d, f, g, -b, c `-=` a, d, f, g, . not correct.
(b) `(Pnn(QnnR)-=a, b, c, d, nnc, f-=c` not correct.
(c ) `(PnnQ)nn(PnnR)-=` regions b, c, `nn` region, c, d, `-=` c, so not correct
(d) `(PnnQ)uu(PnnR)-=" region b, c,"uuc, d-=b,c,d` so correct.