Venn Diagrams_

A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) Operating systems. The following data gives the number of books that contain material on these topics: $n(P) = 8, n(Q) = 13, n(R) = 13, n(P \cap R) = 3, n(P \cap R) = 3, n(Q \cap R) = 3, n(Q \cap R) = 6, n(P \cap Q \cap R) = 2 $ where $n(x)$ is the cardinality of the set $x$. Then the number of text books that have no material on compilers is

Let $\bar{P}$ and $\bar{Q}$ denote the complements of two sets P and Q. Then the set $(P-Q)\cup (Q-P) \cup (P \cap Q)$ is

In a class of 100 students, 55 passed in Mathematics and 67 passed in Physics.The number of students who passed in Physics only is: