Set theory practice · Mixed difficulty

If $R$ and $R^{\prime}$ are symmetric relations (not disjoint) on a set $A$, then the relation $R \cap R^{\prime}$ is

If $A,B$ and $C$ are three non-empty sets such that $A$ and $B$ are disjoint and the number of elements contained in $A$ is equal to those contained in the set of elements common to the sets $A$ and $C$, then $n\left( {A \cup B \cup C} \right)$ is necessarily equal to

If $n\left( u \right) = 100,n\left( A \right) = 50,\;n\left( B \right) = 20$ and $n\left( {A \cap B} \right) = 10,$ then $n\left\{ {{{\left( {A \cup B} \right)}^c}} \right\}$

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

Let $A$ and $B$ be two sets that $A \cap X=B \cap X=\phi$ and $A \cup X=B \cup X$ for some set $X$. Then,

If $A$ and $B$ are two sets, then $A \cap \left( {A \cup B} \right)$ equals

In a certain town 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone.

Consider the following statements in this regard:

1. 10 % families own both a car and a phone

2. 35 % families own either a car or a phone

3. 40,000 families live in the town

Which of the following statements are correct?

Let $A$ be a set represented by the squares of natural number and $x,y$ are any two elements of $A$. Then,

If $A=\left\{(x, y): x^2+y^2 \leq 1, x, y \in R\right\}$ and $B=\left\{(x, y): x^2+y^2 \leq 4 ; x, y \in R\right\}$, then

Let $P=\{\theta: \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and, $Q=\{\theta: \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets. Then,

If $A = \left\{ {1,\;2,\;3,\;4,\;5} \right\},\;B = \left\{ {2,\;4,\;6} \right\},\;C = \left\{ {3,\;4,\;6} \right\}$, then $\left( {A \cup B} \right) \cap C$ is

Let S = {1, 2, 3, … , 100}. The number of non – empty subsets A of S such that the product of elements in A is even, is

Let $S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\}$ and $T=\left\{x \in Z: x^2-7|x|+9 \leq 0\right\}$. Then the number of elements in $S \cap T$ is

If $n(A)=115, n(B)=326, n(A-B)=47$, then what is $n(A \cup B)$ equal to?

Which of the following is true?

Let $A$ be a set containing 10 distinct elements, the total number of distinct functions from $A$ to $A$ is

Given $n\left( U \right) = 20,\;n\left( A \right) = 12,\;n\left( B \right) = 9,n\left( {A \cap B} \right) = 4$, where $U$ is the universal set, $A$ and $B$ are subsets of $U$, then $n\left[ {{{\left( {A \cup B} \right)}^c}} \right]$ equals to

In a B School there are 15 teachers who teach marketing or finance. Of these, 8 teach finance and 4 teach both marketing and finance. How many teach marketing but not finance?

Let $n\left( \mathcal{U} \right) = 700,\;n\left( A \right) = 200,\;n\left( B \right) = 300$ and $n\left( {A \cap B} \right) = 100.$ Then, $n\left( {{A^c} \cap {B^c}} \right) =$

Consider the following statements.
I. If $A_{n}$ is the set of first $n$ prime numbers, then $\bigcup\limits_{{n=2}}^{10} A_{n}$ is equal to $\{2,3,5,7,11,13,17,19,23,29\}$
II. If ${A}$ and ${B}$ are two sets such that ${n}({A} \cup {B})=50$, ${n}({A})=28, {n}({B})=32$, then ${n}({A} \cap {B})=10$.
Which of these is correct?

In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only?

Which of the following collection is a set?

Consider the following statements.

I. $\phi \in\{\phi\} \quad$ II. $\{\phi\} \subseteq \phi$

Which of the statements given above is/are correct?

Suppose $A_1, A_2, A_3, \ldots \ldots \ldots, A_{30}$ are thirty sets each having 5 elements and $B_1, B_2, \ldots \ldots ., B_n$ are $n$ sets each with 3 elements. Let $\bigcup_{i=1}^{30} A_i=\bigcup_{j=1}^n B_j=S$ and each elements of $S$ belongs to exactly 10 of the $A_i^{\prime} s$ and exactly 9 of the $B_j^{\prime} s$. Then $n$ is equal to:

${X}$ and ${Y}$ are two sets such that $n({X})=17, n({Y})=23$, $n({X} \cup {Y})=38$ then $n({X} \cap {Y})$ is

The set $(A \backslash B) \cup(B \backslash A)$ is equal to

In a class of 60 students, 34 have passed in Mathematics and 38 in physics. If each of the students pass at least in one of the subjects, then the number of students who have passed in physics only is

Universal set, $U = \left\{ {x:{x^5} - 6{x^4} + 11{x^3} - 6{x^2} = 0} \right\}$ And $A = \left\{ {x:{x^2} - 5x + 6 = 0} \right\}$
$\;B = \left\{ {x:{x^2} - 3x + 2 = 0} \right\}$
Then, ${\left( {A \cap B} \right)^\prime }$ is equal to

If $A, B, C$ be three sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$, then

Let $A$ and $B$ two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$ then