Set theory practice · Mixed difficulty

If $a\;N = \left\{ {a\;x\;:x \in N} \right\}$ and $b\;N\; \cap c\;N = d\;N,$ where $b,c \in N$ are relatively prime, then

$A=\{x / x \in R,|x|<1\} \quad B=\{x / x \in R,|x-1| \geq 1\}$ 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?

If $X=\left\{8^n-7 n-1: n \in N\right\}$ and $Y=\{49(n-1): n \in N\}$, then

Let $N$ be the set of natural numbers and for $a \in N, a N$ denotes the set $\{a x: x \in N\}.$ If $b N \cap c N=d N,$ where $b, c, d$ are natural numbers greater than 1 and the greatest common divisor (GCD) of $b$ and $c$ is 1, then $d$ equals

If $X = \left\{ {{4^n} - 3n - 1\;:n \in N} \right\}$ and $Y = \left\{ {9\left( {n - 1} \right):n \in N} \right\},$ then $X \cup Y$ is equal to

If $A = \{ x\;:x\;$ is a multiple of $\;3\}$ and,
$B = \{ x\;:x\;$ is a multiple of 5}, then $A - B$ is

Let $A$ and $B$ be two sets such that $A \cup B=A$. Then, $A \cap B$ is equal to

If ${A_1} \subset {A_2} \subset {A_3} \subset \ldots \subset {A_{50}}$ and $n\left( {{A_i}} \right) = i - 1,$ then $n\left( { \cap _{i = 11}^{50}{A_i}} \right) =$

The number of elements in the set $S=\left\{x \in \mathbb{R}: 2 \cos \left(\frac{x^2+x}{6}\right)=4^x+4^{-x}\right\}$ is :

$\left\{ {n\left( {n + 1} \right)\left( {2n + 1} \right):n \in Z} \right\} \subset$ subset

In a group of 70 people, 37 like coffee, 52 like tea and each person like atleast one of the two drinks. The number of persons liking both coffee and tea is

If $A = \{ x\;:x$ is a multiple of 4} and,
$B = \{ x\;:x\;$ is a multiple of $\;6\}$, then $A \cap B$ consists of multiples of

If ${A}=\{x \in {R} / {f}(x)=0\}$ and ${B}=\{x \in {R} / {g}(x)=0\}$ then ${A} \cap {B}=$

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

Consider the set $A$ of all determinants of order 3 with entries 0 or 1 only. Let $B$ be the subset of $A$ consisting of all determinants with value 1. Let $C$ be the subset of the set of all determinants with value $- 1.$Then

Which one of the following is not true?

If the cardinality of a set $A$ is 4 and that of a set $B$ is 3 , then what is the cardinality of the set $A \triangle B$ ?

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?

Let $Y=\{1,2,3,4,5,6,7\}, A=\{3,4\}, B=\{1,2,5\}$, then $(Y \times A) \cap(Y \times B)$ is

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?

In an election, two contestants $A$ and $B$ contested $x\,\%$ of the total voters voted for $A$ and $\left( {x + 20} \right)\%$ for $B$. If 20% of the voters did not vote, then $x =$

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 $A = \left\{ {\left( {x,y} \right)\;:y = \frac{4}{x},x \ne 0} \right\}$ and
$B = \left\{ {\left( {x,y} \right):{x^2} + {y^2} = 8,x,y \in R} \right\}$, then

Consider the following relations:

I. $A-B=A-(A \cap B)$

II. ${A}=({A} \cap {B}) \cup({A}-{B})$

III. $A-(B \cup C)=(A-B) \cup(A-C)$

Which of these is/are correct?

If $X \cup\{3,4\}=\{1,2,3,4,5,6\}$ then which of the following is true