Set theory practice · Mixed difficulty

The number of elements of the power set of a set containing $n$ elements is

If $A=\{1,2,5\}$ and $B=\{3,4,5,9\}$, then $A \Delta B$ is equal to

$A$ and $B$ are any two non-empty sets and $A$ is proper subset of $B$. If $n\left( A \right) = 5,$ then find the minimum possible value of $n\left( {A\Delta B} \right)$

Which one of the following is $(A-B) \cup(B-A)$ ?

In a rehabilitation programme, a group of 50 families were assured new houses and compensation by the government. Number of families who got both is equal to the number of families who got neither of the two. The number of families who got new houses is 6 greater than the number of families who got compensation. How many families got houses?

If $A=\{2,3,4,8,10\}, B=\{3,4,5,10,12\}$ and $C=\{4, 5,6,12,14\}$, then $(A \cap B) \cup(A \cap C)$ is equal to

The finite sets $A$ and $B$ have m and n elements respectively. if the total number of subsets of $A$ is 112 more than the total number of subsets of $B$, then the volume of $m$ is

If $A=\{1,2,3\}$ and $B=\{3,8\}$, then $(A \cup B) \times(A \cap B)$ is

If a set $A=\{a, b, c\}$ then the number of subsets of the set $A$ is

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B.$ Then the distance of the point $P(m, n)$ from the point $Q(-2,-3)$ is:

If $A$ and $B$ are any two sets, then $A \cup(A \cap B)$ is equal to:

If ${U}=\{1,2,3\}$ and ${A}=\{1,2\}$ then $[{P}({A})]^{\prime}=$

If ${S}$ and ${T}$ are two sets such that ${S}$ has 21 elements, ${T}$ has 32 elements, and ${S} \cap {T}$ has 11 elements, then number of elements ${S} \cup {T}$ has

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If $K$% of them are suffering from both ailments, then $K$ cannot belong to the set

Let $A$ and $B$ have 3 and 6 elements respectively. What can be the minimum number of elements in $A \cup B?$

Let $P=\{1,2,3, \ldots, 100\}$ be the number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is

20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is

Suppose ${A_1},\;{A_2}, \ldots ,{A_{30}}$ are thirty sets, each having 5 elements and ${B_1},\;{B_2},\; \ldots ,\;{B_n}$ are $n$ sets each with 3 elements, let
$\mathop \cup \nolimits_{i = 1}^{30} {A_i} = \mathop \cup \nolimits_{j = 1}^n {B_j} = S$ and each element of S belongs to exactly 10 of the ${A_i}{\,^\prime }s$ and exactly 9 of the ${B_j}$ 's. Then, $n$ is equal to

There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:

A set $\mathrm{S}$ contains 3 elements, the number of subsets of which of following sets is 256 .

Let $R$ be a relation on $\mathbf{N}$ defined by $R=\left\{(m, n): m, n \in N \text { and } m=n^2\right\}.$
Which of the following is true.

If $A=\left\{\theta: 2 \cos ^2 \theta+\sin \theta \leq 2\right\}$ and $B=\left\{\theta: \frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{2}\right\}$, then $A \cap B$ is equal to

The value of $n\left[ {P\left( {P\left( {P\left( \phi \right)} \right)} \right)} \right]$ is equal to

Let $S = \left\{ {1,\;2,\;3,\;4} \right\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

Let $\mathrm{X=}\{1,2,3,4,5\}$. The number of different ordered pairs $(\mathrm{Y}, \mathrm{Z})$ that can formed such that $\mathrm{Y} \subseteq \mathrm{X}, \mathrm{Z} \subseteq \mathrm{X}$ and $\mathrm{Y} \cap \mathrm{Z}$ is empty is:

If $A = \left\{ {1,\;2,\;3,\;4} \right\},$ then the number of subsets of $A$ that contain the element 2 but not 3, is

If $A=\{x: x=3 n, n \in Z\}$ and $B=\{x: x=4 n, n \in Z\}$ then $A \cap B$ is

If $A=\{2,4\}$ and $B=\{3,4,5\}$, then $(A \cap B) \times(A \cup B)$ is

The cardinality of the set $\mathrm{P}\{\mathrm{P}[\mathrm{P}(\phi)]\}$ is

If $A$ and $B$ are two sets such that $n\left( A \right) = 7,n\left( B \right) = 6$ and $\left( {A \cap B} \right) \ne \phi .$ Then the greatest possible value of $n\left( {A\;\mathrm{\Delta \;}B} \right),$ is