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Relation, Number of relation - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
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21 Questions around this concept.
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For $A=\{1,2\}$ and $B=\{a, b, c\}$, then relation $R$ from $A$ to $B$ is :
How many relations can be made from set $A$ to set $B$ where $n(A)=5$ and $n(B)=2$?
The identity element for the binary operation * defined on Q ~ {0} as a * b = 2 ab a, b Q ~ {0} is
Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A \times B$ such that $R=\left(\left(a_1 b_1\right),\left(a_2 b_2\right)\right): \mathrm{a}_1 \leq \mathrm{b}_2$ and $\left.\mathrm{b}_1 \leq \mathrm{a}_2\right\}$. Then the number of elements in the set R is
Concepts Covered - 1
Relation, Number of relation
A relation $R$ from a non-empty set $A$ to a non-empty set $B$ is a subset of the cartesian product $A \times B$.
The subset is derived by describing the relationship between the first element and the second element of the ordered pairs in $\mathrm{A} \times \mathrm{B}$.
The second element is called the image of the first element.
If the element $(a, b)$ belongs to $R$, (here $a$ belongs to $A$ and $b$ belongs to $B$ ), then the relation is represented as a R b.
Number of Relations from A to B
If $A$ has $m$ elements and $B$ has $n$ elements, then $A \times B$ has $m \times n$ elements.
As the number of subsets of $A x B$ is $2^{m n}$, and a relation is a subset of $A x B$, so the total number of relations from $A$ to $B$ will be $2^{\mathrm{mn}}$
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