(B) Given that the number of elements in set $A$ is $n(A) = p$ and the number of elements in set $B$ is $n(B) = q$. The total number of elements in th

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(B) Given that the number of elements in set $A$ is $n(A) = p$ and the number of elements in set $B$ is $n(B) = q$. The total number of elements in the Cartesian product $A \times B$ is $n(A \times B) = n(A) \times n(B) = pq$. $A$ relation from set $A$ to set $B$ is a subset of $A \times B$. The total number of subsets of a set with $n$ elements is $2^n$. Therefore,the total number of relations from set $A$ to set $B$ is $2^{pq}$.

Class 11 Mathematics Relations and Functions Relations

Easy

Let the number of elements of the sets $A$ and $B$ be $p$ and $q$,respectively. Then,the number of relations from the set $A$ to the set $B$ is

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A
$2^{p+q}$
B
$2^{pq}$
C
$p+q$
D
$pq$

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Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ from $A$ to $B$ is defined as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find the inverse relation ${R^{ - 1}}$.

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Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

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Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$,and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a relation from $A$ to $B$? Justify your answer.

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$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then ${R^{ - 1}}$ is

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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 $R$.

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Let the number of elements of the sets $A$ and $B$ be $p$ and $q$,respectively. Then,the number of relations from the set $A$ to the set $B$ is

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Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ from $A$ to $B$ is defined as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find the inverse relation ${R^{ - 1}}$.

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