Set Theory Questions with Solutions

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

There are two sets A and B with $\left|A\right|=m$ and $\left|B\right|=n$. If $\left|P\left(A\right)\right|-\left|P\left(B\right)\right|=112$, then choose the wrong option (where $\left|A\right|$ denotes the cardinality of A, and $P\left(A\right)$ denotes the power set of A).

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

Let $A=5^n-4n-1:n\in N$ and $B=16\left(n-1\right):n\in N$ be sets. Then

Suppose that $C$ represents the set of all countries, $R$ the set of all countries that have at least one river flowing through it, $M$ the set of all countries that have at least one mountain in it, and $D$ the set of all countries that have at least one desert in it. It is given that $R\cup M\cup D=C$. Which one of the following gives the set of all countries that have either a mountain or a river, but do not have a desert in it? The notation $D^c$ represents the complement of $D$ with respect to the universal set $C$.