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

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Solution

The correct option is B $7$
$(a, b) R (c, d)$ iff $a d = b c$
$(a, b) R (4, 3) \Rightarrow 3 a = 4 b$
$\Rightarrow a = \frac{4 b}{3}$
$b$ must be multiple of $3.$
$b$ can be $3, 6, 9, \dots, 30$
Also, $a$ must be less than or equal to $30.$
So $(a, b)$ can be $(4, 3), (8, 6), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)$
$\Rightarrow 7$ ordered pairs

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Q. Let A = {2, 3, 4, 5, ..., 17, 18}. Let '≃' be the equivalence relation on A × A, cartesian product of A with itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is
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Q. Let R be a relation on the set A of ordered pair of integers defined by (x, y) R (u, v) if xv = yu. Show that R is an equivalence relation.

Let $A = \{2, 3, 4, 5, . ., 30\}$ and $' ≅'$ be an equivalence relation $A \times A$ , defined by $(a, b) ≅ (c, d)$ , if and only if $a d = b c$ . Then the number of ordered pair $(4, 3)$ is equal to:

Q. Let

A = {2, 3, 4, 5....17, 18} .

Let

≃

be the equivalence relation on

A \times A,

cartesian product of

A

with itself, defined by

(a, b) ≃ (c, d)

a d = b c .

Then the number of ordered pairs of the equivalence class of

(3, 2)

Q. Let

A = {2, 3, 4, 5, . . ., 17, 18} .

Let

≃

be the equivalence relation on

A \times A,

cartesian product of

A

with itself, defined by

(a, b) ≃ (c, d)

a d = b c .

Then the number of ordered pairs of the equivalence class of

(3, 2)

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

The correct option is B 7(a,b) R (c,d) iff ad=bc (a,b) R (4,3)⇒3a=4b ⇒a=4b3 b must be multiple of 3. b can be 3,6,9,…,30 Also, a must be less than or equal to 30. So (a,b) can be (4,3),(8,6),(12,9),(16,12),(20,15),(24,18),(28,21) ⇒7 ordered pairs

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