Set Theory Questions with Solutions

The set $\left(A\Delta B\right)\cap C$ is not equal to:

If $X=4^n-3n-1\mid n\in N$ and $Y=9\left(n-1\right)\mid n\in N$, then

A set contains $\left(2n+1\right)$ elements. If the number of subsets that contain at most $n$ elements is $4096$, then the value of $n$ is:

If $P=4^n-3n-1:n\in N$ and $Q=9n-9:n\in N$, then $P\cup Q$ equals:

$A_1,A_2,A_3,A_4$ are subsets of a set $U$ containing 75 elements. Each $A_i$ has 28 elements, any two of them have 12 elements in common, any three have 5 elements in common and all four have 1 element in common. The number of elements belonging to none of the four subsets is:

Suppose $P_1,P_2,\dots ,P_{30}$ are thirty sets each having $5$ elements and $Q_1,Q_2,\dots ,Q_n$ are $n$ sets with $3$ elements each. Let ${\bigcup }_{i=1}^{30}{P}_i={\bigcup }_{j=1}^n{Q}_j=S$ and each element of $S$ belongs to exactly $10$ of the $P_i$ 's and exactly $9$ of the $Q_j$ 's. Then $n$ equals

Suppose $A_1,A_2,\dots ,A_{30}$ are 30 sets, each with five elements, and $B_1,B_2,\dots ,B_n$ are $n$ sets, each with three elements, such that ${\bigcup }_{i=1}^{30}{A}_i={\bigcup }_{j=1}^n{B}_j=S$, and each element of S belongs to exactly ten of the $A_i$ 's and exactly nine of the $B_j$ 's. Then $n=$

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).

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 $C$.