Which one is the superset?

Important Questions on Sets

MEDIUM

Mathematics>Algebra>Sets>Subsets

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $48$ more than the total number of subsets of the second. The values of $m$ and $n$ respectively, are

MEDIUM

Mathematics>Algebra>Sets>Subsets

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

EASY

Mathematics>Algebra>Sets>Subsets

If $A$ and $B$ are two non-empty finite sets having $3$ and $4$ elements respectively, then what would be the possible number of subsets of $A\times B?$

MEDIUM

Mathematics>Algebra>Sets>Subsets

Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A\times B$ having $3$ or more elements is :

EASY

Mathematics>Algebra>Sets>Subsets

Let $S=\left\{1, 2, 3, \dots .,100\right\}$, then number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is :

EASY

Mathematics>Algebra>Sets>Subsets

If $A=\left\{1,2,3,\dots \dots 10\right\}$ then number of subsets of $A$ containing only odd numbers is

HARD

Mathematics>Algebra>Sets>Subsets

There is a set $P$ of ordered pairs in which each pair has a vowel as first element and a consonant as second element. It is given that $M=4^{10}.$ How many elements will be there in power set of $P$ ?

EASY

Mathematics>Algebra>Sets>Subsets

Verify $A\subset B$ for the sets $A=\left\{a, b, c\right\}, B=\left\{1, \left\{a, b, c\right\}, 2\right\}$. If not justify your answer.

EASY

Mathematics>Algebra>Sets>Subsets

If a set $A$ has $4$ elements, then the total number of proper subsets of set $A$, is

EASY

Mathematics>Algebra>Sets>Subsets

The number of proper subsets of a set having $n+1$ elentents is

HARD

Mathematics>Algebra>Sets>Subsets

Let $A$ and $B$ be two sets containing four and two elements respectively. Then the number of subsets of the set $A\times B$, each having at least three elements is

EASY

Mathematics>Algebra>Sets>Subsets

Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is $112$ more than that of the second. The values of $m$ and $n$ are respectively

HARD

Mathematics>Algebra>Sets>Subsets

A positive integer $k$ is said to be good if there exists a partition of $\left\{1,2,3,\dots .,20\right\}$ into disjoint proper subsets such that the sum of the numbers in each subset of the partition is $k.$ How many good numbers are there?

MEDIUM

Mathematics>Algebra>Sets>Subsets

Two 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 value of $m$ is

MEDIUM

Mathematics>Algebra>Sets>Subsets

Let $A$ and $B$ be two finite sets such that there are exactly $144$ sets which are subsets of $A$ or subsets of $B.$ Find the number of elements in $A\cup B.$

MEDIUM

Mathematics>Algebra>Sets>Subsets

Let $A=\left\{1,2,3,4,5,6,7\right\}$ and $B=\left\{3,6,7,9\right\}$. Then the number of elements in the set $\left\{C\subseteq A:C\cap B\ne \varphi \right\}$ is ______

MEDIUM

Mathematics>Algebra>Sets>Subsets

Set $A$ has $m$ elements and set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m·n$ is___.

EASY

Mathematics>Algebra>Sets>Subsets

The total number of subsets of the set $\{1, 2, \dots \dots ,10\}$ which do not contain the element $6$ is

EASY

Mathematics>Algebra>Sets>Subsets

If the total number of $m$-element subsets of the set $A=\left\{a_1,a_2,\dots ,a_n\right\}$ is $k$ times the number of $m$ element subsets containing $a_4$, then $n$ is

HARD

Mathematics>Algebra>Sets>Subsets

Let $Z$ be the set of integers. If $A=\left\{x\in Z: 2^{\left(x+2\right)\left(x^2-5x+6\right)}=1\right\}$ and $B=\{x\in Z:-3<2x-1<9\}$, then the number of subsets of the set $A\times B$, is :