Sets and Relations · Mathematics · KCET

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 $A=\{2,3,4,5, \ldots, 16,17,18\}$. 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 pairs of the equivalence class of $(3,2)$ is

Which of the following is an empty set?

Let the relation $$R$$ be 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 $$p^2+q^2=$$

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

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 $$n(A)=2$$ and total number of possible relations from Set A to set B is 1024, then $$n(B)$$ 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 $$A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}$$, then the number of onto functions from $$A$$ to $$B$$ is

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 $$U$$ 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 $$n\left(A^{\prime} \cap B^{\prime}\right)=$$