Let $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.
Let $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.
It is given that $A=\{x, y, z\}$ and $B=\{1,2\}$
$\therefore A \times B=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}$
Since $n(A \times B)=6,$ the number of subsets of $A \times B$ is $2^{6}$
Therefore, the number of relations from $A$ to $B$ is $2^{6}$.
Similar Questions
The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by
The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by
Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $
Find the domain of $R$
Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $
Find the domain of $R$
Let $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that
$(a, b) \in R$ and $(b, c) \in R$ implies that $(a, c) \in R$
Let $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that
$(a, b) \in R$ and $(b, c) \in R$ implies that $(a, c) \in R$
Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Depict this relation using an arrow diagram.
Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Depict this relation using an arrow diagram.
Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Write down the domain, codomain and range of $R .$
Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Write down the domain, codomain and range of $R .$