Let A = {2, 3, 4, 5, ldots, 30} and simeq be | vedclass

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

Question

(D) Given the set $A = \{2, 3, 4, 5, \ldots, 30\}$.The equivalence relation is defined as $(a, b) \simeq (c, d)$ if and only if $ad = bc$.We need to f

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(D) Given the set $A = \{2, 3, 4, 5, \ldots, 30\}$.The equivalence relation is defined as $(a, b) \simeq (c, d)$ if and only if $ad = bc$.We need to find the number of ordered pairs $(c, d)$ such that $(c, d) \simeq (4, 3)$.Using the definition,we have $c 	imes 3 = d 	imes 4$,which implies $\frac{c}{d} = \frac{4}{3}$.This means $c = 4k$ and $d = 3k$ for some constant $k$,where $c, d \in A$.Since $c, d \in \{2, 3, \ldots, 30\}$,we check the possible values for $k$:For $k=1: (c, d) = (4, 3)$For $k=2: (c, d) = (8, 6)$For $k=3: (c, d) = (12, 9)$For $k=4: (c, d) = (16, 12)$For $k=5: (c, d) = (20, 15)$For $k=6: (c, d) = (24, 18)$For $k=7: (c, d) = (28, 21)$For $k=8: (c, d) = (32, 24)$,which is not possible since $32 
otin A$.Thus,the possible ordered pairs are $(4, 3), (8, 6), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)$.The total number of such ordered pairs is $7$.

Let $A = \{2, 3, 4, 5, \ldots, 30\}$ and $\simeq$ be an equivalence relation on $A \times A$,defined by $(a, b) \simeq (c, d)$ if and only if $ad = bc$. Then the number of ordered pairs $(c, d)$ which satisfy this equivalence relation with the ordered pair $(4, 3)$ is equal to:

Similar Questions

Let $R$ be a relation defined on $N$ such that $a R b$ if $2a + 3b$ is a multiple of $5$,where $a, b \in N$. Then $R$ is

The relation "less than" in the set of natural numbers is

For any two real numbers $\theta$ and $\phi$, we define $\theta R \phi$ if and only if $\sec^{2} \theta - \tan^{2} \phi = 1$. The relation $R$ is

Let $A = \{2, 3, 6, 7\}$ and $B = \{4, 5, 6, 8\}$. Let $R$ be a relation defined on $A \times B$ by $(a_1, b_1) R (a_2, b_2)$ if and only if $a_1 + a_2 = b_1 + b_2$. Then the number of elements in $R$ is ...........

The number of non-empty equivalence relations on the set $\{1, 2, 3\}$ is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module