Set Theory Questions with Solutions

If there are 5 sets represented via a Venn diagram, the number of regions that arise in the Venn diagram equals:

In a Venn diagram, what does the overlapping region of two sets $A$ and $B$ represent?

Let A and B be sets such that $A\cap X=B\cap X=\varphi$ and $A\cup X=B\cup X$ for some set X. Then

Find the number of elements in the union of 4 sets A, B, C and D having 150, 180, 210 and 240 elements respectively, given that each pair of sets has 15 elements in common, each triple of sets has 3 elements in common and $A\cap B\cap C\cap D=\varnothing$.

Let $X$ be the universal set for sets $A$ and $B$. If $n\left(A\right)=200$, $n\left(B\right)=300$ and $n\left(A\cap B\right)=100$, then $n\left(A\prime \cap B\prime \right)=300$ provided $n\left(X\right)$ is equal to

In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is

How many proper subsets of $1,2,3,4,5,6,7$ contain the numbers $1$ and $7$?

If A is a subset of B and B is a subset of C, then cardinality of $A\cup B\cup C$ is equal to

In a class of 50 students, it was found that 30 students read "Hitavad", 35 students read "Hindustan" and 10 read neither. How many students read both "Hitavad" and "Hindustan" newspapers?

If $A=x,y,z$, then the number of subsets in powerset of A is

If $A=1,2,3,4$ and $B=3,4,5$, then the number of elements in $\left(A\cup B\right)\times \left(A\cap B\right)\times \left(A\Delta B\right)$ is

If X and Y are two sets, then $X\cap Y\prime \cap \left(X\cup Y\right)\prime$ is

If the sets A and B are defined as A = {(x, y) | y = 1/x, 0 ≠ x ∈ R}, B = {(x, y) | y = −x, x ∈ R}, then

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

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: $n\left(P\right)=8$, $n\left(Q\right)=13$, $n\left(R\right)=13$, $n\left(P\cap Q\right)=3$, $n\left(P\cap R\right)=3$, $n\left(Q\cap R\right)=6$, $n\left(P\cap Q\cap R\right)=2$, where $n\left(X\right)$ is the cardinality of the set $X$. Then the number of text books that have no material on compilers is

The number of elements in the power set P(S) of the set S = {2, (1, 4)} is

In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover, 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business, 8 students liked both Business and Literature, and 5 students liked all three subjects. Then the number of students who liked exactly one subject is

In a beauty contest, half the number of experts voted for Mr. A and two-thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all?

Let Z be the set of all integers, and consider the sets $X=\left(x,y\right):x^2+2y^2=3,x,y\in Z$ and $Y=\left(x,y\right):x>y,x,y\in Z$. Then the number of elements in $X\cap Y$ is