Sets and Relations

If $A = \{a, b, c, d, e, f\}$, then the number of subsets of A which contains at least $2$ elements is

If $A = \{1, 2, 3, 4, \ldots, 10\}$, then the number of non-empty subsets of A containing only even number is

If $n(A) = 2$ and the number of relations from set A to set B is $1024$, then $n(B)$ is

Let R be the relation in the set $\mathbb{N}$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is the correct answer?

Consider the following statements :
Statement(I) : The set of all solutions of the linear inequalities $3 \mathrm{x}+8<17$ and $2 \mathrm{x}+8 \geq 12$ are $\mathrm{x}<3$ and $x \geq 2$ respectively.
Statement(II) : The common set of soluti...

\(\text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is }\)

$A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements.
Statement (I): Minimum number of elements in AUB is 3
Statement (II): Maximum number of elements in AB is 3 Which of the following is correct?

If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}\right.$ is an integer and $\left.\mathrm{x}^2-9=0\right\}$
$B=\{x: x$ is a natural number and $2 \leq x<5\}$
$\mathrm{C}=\{\mathrm{x}: \mathrm{x}$ is a prime number $\leq 4\}$
Then $(B-C) \cup A$...

Let $A=\{2,3,4,5, \ldots, 16,17,18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R(c, d)$ if and only if $a d=b c$ for all $(a, b),(c, d)$ in $A \times A$. Then, the number of ordered pa...

Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of $m$ and $n$, respectively are

Let the relation \(R\) be defined in \(N\) by \(a R b\), if \(3 a+2 b=27\), then \(R\) is

Which of the following is an empty set?

Let the relation \(R\) is defined in \(N\) by \(a R b\), if \(3 a+2 b=27\) then \(R\) is

Suppose that the number of elements in set \(A\) is \(p\), the number of elements in set \(B\) is \(q\) and the number of elements in \(A \times B\) is 7, then \(p^2+q^2=\)

In a certain two \(65 \%\) families own cell phones, 15000 families own scooter and \(15 \%\) families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

If \(A=\{1,2,3,4,5,6\}\), then the number of subsets of A which contain at least two elements is

If a relation \(R\) on the set \(\{1,2,3\}\) be defined by \(R=\{(1,1)\}\), then \(R\) is

If \(A=\{a, b, c\}\), then the number of binary operations on \(A\) is

If \(n(A)=2\) and total number of possible relations from Set A to set B is 1024, then \(n(B)\) is

If \(U\) is the universal set with 100 elements; \(A\) and \(B\) are two set such that \(n(A)=50, n(B)=60, n(A \cap B)=20\) then \(n\left(A^{\prime} \cap B^{\prime}\right)=\)

On the set of positive rational, a binary operation * is defined by \(a * b=\frac{2 a b}{5}\). If \(2 * x=3^{-1}\), then \(x=\)

If \(A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}\), then the number of onto functions from \(A\) to \(B\) is

If $A$ and $B$ are finites sets and $A \subset B$, then