Set theory practice · Medium

If $A$ and $B$ are two disjoint sets, then which one of the following is correct?

The set $\{x: x$ is a positive integer less than 6 and $3^x-1$ is an even number $\}$ in roster form is

20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics, while 4 teach both the subject. Then, the number of teachers teaching Physics only is

The set $A=\left\{x: x^4-x^3-x^2=0\right.$ and $\left.x \in N\right\}$ represents

In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. If each student has taken either Mathematics or Economics or both, then the number of students who have taken Economics but not Mathematics is

Let $P(S)$ denote the power set of $S=\{1,2,3, \ldots, 10\}$. Define the relations $R_{1}$ and $R_{2}$ on $P(S)$ as $A R_{1} B$ if $\left(A \cap B^{C}\right) \cup\left(B \cap A^{C}\right)=\phi$ and $A R_{2} B$ if $A \cup B^{C}=B \cup A^{C}, \forall A, B \in P(S)$. Then

Let $S=\{x \in R: x \geq 0$ and $2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0$. Then $S$:

Let $A = \left\{ {{\text{ONGC}},{\text{BHEL}},{\text{SAIL}},{\text{GAIL}},{\text{IOCL}}} \right\}$ and $R$ be a relation defined as “two elements of $A$ are related if they share exactly one letter”. The relation $R$ is

In a class of 55 students, the number of students studying different subjects are 23 in mathematics, 24 in physics, 19 in chemistry, 12 in mathematics and physics, 9 in mathematics and chemistry, 7 in physics and chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is:

Let $\mathrm{A}=\{\mathrm{x} \in \mathrm{W}$, the set of whole numbers and $x < 3\}, B=\{x \in N$, the set of natural numbers and $2 \leq x < 4\}$ and $C=\{3,4\}$, then how manyelements will $(\mathrm{A} \cup \mathrm{B}) \times \mathrm{C}$ contain?

Let $S=\left\{\theta \in[0,2 \pi]: 2 \cos ^2 \theta+3 \sin \theta=0\right\}$ then number of elements of $S$ is

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

If $A = \left\{ {p \in N:p\;\mathrm{is\;}a\mathrm{\;prime\;and\;}p = \frac{{7{n^2} + 3n + 3}}{n}\mathrm{\;for\;some}\;n \in N} \right\},$ then the number of elements in the set $A$, is

$A$ 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 $n\left( {A\Delta B} \right)$

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

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

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:

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

$A=\{x / x \in R,|x|<1\} \quad B=\{x / x \in R,|x-1| \geq 1\}$ and $A \cup B=R-D$ Then $D=$

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

Which of the following is the empty set?

Let $\mathrm{A}=\{1,2\}, \mathrm{B}=\{3,4\}$. Then, number of subsets of $\mathrm{A} \times \mathrm{B}$ is

If $A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} = 4;\;x,y \in R} \right\}$ and
$B = \left\{ {\left( {x,y} \right):{x^2} + {y^2} = 9;x,y \in R} \right\}$, then

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

If $A, B$ and $C$ are three finite sets, then what is $[(A \cup B) \cap C]$ equal to?

If $X$ and $Y$ are two sets such that $(X \cup Y)$ has 60 elements, $X$ has 38 elements and $Y$ has 42 elements, how many elements does $(\mathrm{X} \cap \mathrm{Y})$ have?

If $A \cup B=A \cup C$ and $A \cap B=A \cap C$, 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 $n(A)=4$ and $n(B)=7$, then the minimum and maximum value of $n(A \cup B)$ are, respectively

Let $A=\{x: x$ is a digit in the number 3591$\}$, $B=\{r: x \in N, x<10\}$.
Which of the following is false?