Let R be a relation from A = {2, 3, 4, 5} to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The relation $R$ is defined as $R = \{(a, b) \mid a 	ext{ divides } b, a \in A, b \in B\}$.We check each element $a \in A$ to see which $b \in B$

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) The relation $R$ is defined as $R = \{(a, b) \mid a 	ext{ divides } b, a \in A, b \in B\}$.We check each element $a \in A$ to see which $b \in B$ it divides:For $a = 2$: $2$ divides $6$ and $10$,so $(2, 6) \in R$ and $(2, 10) \in R$.For $a = 3$: $3$ divides $3$ and $6$,so $(3, 3) \in R$ and $(3, 6) \in R$.For $a = 4$: $4$ does not divide any element in $B$.For $a = 5$: $5$ divides $10$,so $(5, 10) \in R$.Thus,$R = \{(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)\}$.The inverse relation $R^{-1}$ is defined as $R^{-1} = \{(b, a) \mid (a, b) \in R\}$.Therefore,$R^{-1} = \{(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)\}$.The number of elements in $R^{-1}$ is the same as the number of elements in $R$,which is $5$.

Let $R$ be a relation from $A = \{2, 3, 4, 5\}$ to $B = \{3, 6, 7, 10\}$ defined by $R = \{(a, b) \mid a \text{ divides } b, a \in A, b \in B\}$. Then,the number of elements in $R^{-1}$ will be:

Similar Questions

Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A$. Then

If $R$ and $R^1$ are equivalence relations on a set $A$, then which of the following is also an equivalence relation?

On the power set $P(A)$ of a set $A$,the relation "is a subset of" $(\subseteq)$ is:

Let $N$ denote the set of all natural numbers. Define two binary relations on $N$ as $R_1 = \{(x,y) \in N \times N : 2x + y = 10\}$ and $R_2 = \{(x,y) \in N \times N : x + 2y = 10\}$. Then

Define a relation $R$ on $A=\{1, 2, 3, 4\}$ as $x R y$ if $x$ divides $y$. $R$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module