Set theory practice · Easy

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

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

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

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

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 ${A} \cap {B}=$

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

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 $A = \left\{ {\left( {x,y} \right)\;:y = \frac{4}{x},x \ne 0} \right\}$ 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?