1. The problem involves identifying the shaded region in a Venn diagram with three sets $P$, $Q$, and $R$ within the universal set $\xi = P \cup Q \cup R$. 2. The shaded region is described as the intersection of $P$ and $Q$ excluding $R$, which can be written as $P \cap Q \cap R^c$ where $R^c$ is the complement of $R$. 3. Among the options given: - A: $P \cup Q \cap R$ means union of $P$ with the intersection of $Q$ and $R$. - B: $P \cup Q \cap R'$ means union of $P$ with the intersection of $Q$ and complement of $R$. - C: $P \cap Q \cup R$ means union of $R$ with the intersection of $P$ and $Q$. - D: $P \cap Q \cap R$ means intersection of all three sets. 4. The correct expression for the shaded region (intersection of $P$ and $Q$ excluding $R$) is $P \cap Q \cap R^c$, which matches option B if we interpret $R'$ as $R^c$. 5. Therefore, the answer is option B: $P \cup Q \cap R'$ is incorrect because it uses union instead of intersection. 6. The correct notation should be $P \cap Q \cap R'$, but since none of the options exactly match this, the closest correct interpretation is option B if the union symbol is a typographical error. 7. Regarding the statements: - Statement 1: $\emptyset = \{0\}$ is false because $\emptyset$ is the empty set with no elements, while $\{0\}$ is a set containing zero. - Statement 2: $n(\emptyset) = 0$ is true because the empty set has zero elements. - Statement 3: $\emptyset$ is a subset of itself is true by definition of subsets. Final answer: The shaded region corresponds to $P \cap Q \cap R^c$. Hence, the correct choice is closest to option B if corrected to intersection: $P \cap Q \cap R'$.