Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$
Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$
We have,
$A \times B=\{(1,3),(1,4),(2,3),(2,4)\}$
Since $n( A \times B )=4,$ the number of subsets of $A \times B$ is $2^{4} .$
Therefore, the number of relations from $A$ into $B$ will be $2^{4}$.
Similar Questions
The Fig shows a relation between the sets $P$ and $Q$. Write this relation
in roster form
What is its domain and range ?
The Fig shows a relation between the sets $P$ and $Q$. Write this relation
in roster form
What is its domain and range ?
Let $S=\{1,2,3,4,5,6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties:
$i$. $R$ has exactly $6$ elements.
$ii$. For each $(a, b) \in R$, we have $|a-b| \geq 2$.
Let $Y=\{R \in X$ : The range of $R$ has exactly one element $\}$ and $Z=\{R \in X: R$ is a function from $S$ to $S\}$.
Let $n(A)$ denote the number of elements in a Set $A$.
(There are two questions based on $PARAGRAPH " 1 "$, the question given below is one of them)
($1$) If $n(X)={ }^m C_6$, then the value of $m$ is. . . .
($2$) If the value of $n(Y)+n(Z)$ is $k^2$, then $|k|$ is. . . .
Give the answer or quetion ($1$) and ($2$)
Let $S=\{1,2,3,4,5,6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties:
$i$. $R$ has exactly $6$ elements.
$ii$. For each $(a, b) \in R$, we have $|a-b| \geq 2$.
Let $Y=\{R \in X$ : The range of $R$ has exactly one element $\}$ and $Z=\{R \in X: R$ is a function from $S$ to $S\}$.
Let $n(A)$ denote the number of elements in a Set $A$.
(There are two questions based on $PARAGRAPH " 1 "$, the question given below is one of them)
($1$) If $n(X)={ }^m C_6$, then the value of $m$ is. . . .
($2$) If the value of $n(Y)+n(Z)$ is $k^2$, then $|k|$ is. . . .
Give the answer or quetion ($1$) and ($2$)
- [IIT 2024]
Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$
Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$
Determine the domain and range of the relation $R$ defined by $R =\{(x, x+5): x \in\{0,1,2,3,4,5\}\}$
Determine the domain and range of the relation $R$ defined by $R =\{(x, x+5): x \in\{0,1,2,3,4,5\}\}$
$A=\{1,2,3,5\}$ and $B=\{4,6,9\} .$ Define a relation $R$ from $A$ to $B$ by $R = \{ (x,y):$ the difference between $ x $ and $ y $ is odd; ${\rm{; }}x \in A,y \in B\} $ Write $R$ in roster form.
$A=\{1,2,3,5\}$ and $B=\{4,6,9\} .$ Define a relation $R$ from $A$ to $B$ by $R = \{ (x,y):$ the difference between $ x $ and $ y $ is odd; ${\rm{; }}x \in A,y \in B\} $ Write $R$ in roster form.