Let A = {1,4, 7} and B = {2, 3, 8}. Then the number of elements, in the relation is ________. [2026]

Question

Let A = {1,4, 7} and B = {2, 3, 8}. Then the number of elements, in the relation $R = {((a_{1}, b_{1}), (a_{2} b_{2})) \in ((A \times B) \times (A \times B)) : a_{1} + b_{2} divides a_{2} + b_{1}}$ is ________. [2026]

Smart Achievers · Accepted Answer

(18)

Given, A = {1, 4, 7} and B = {2, 3,8}

All possible sums:

A/B	2	3	8
1	3	4	9
4	6	7	12
7	9	10	15

$a_{1} + b_{2}$	$a_{2} + b_{1}$	Number of pairs
15	15	1
12	12	1
10	10	1
9	9	4
7	7	1
6	6, 12	2
4	4, 12	2
3	3, 6, 9 12, 15	6

$∴$ Number of relations = 18

Solution

Q.
Let A = {1,4, 7} and B = {2, 3, 8}. Then the number of elements, in the relation $R = {((a_{1}, b_{1}), (a_{2} b_{2})) \in ((A \times B) \times (A \times B)) : a_{1} + b_{2} divides a_{2} + b_{1}}$ is ________. [2026]

Ans.
(18)

Given, A = {1, 4, 7} and B = {2, 3,8}

All possible sums:

A/B 2 3 8

1 3 4 9

4 6 7 12

7 9 10 15

$a_{1} + b_{2}$ $a_{2} + b_{1}$ Number of pairs

15 15 1

12 12 1

10 10 1

9 9 4

7 7 1

6 6, 12 2

4 4, 12 2

3 3, 6, 9 12, 15 6

$∴$ Number of relations = 18

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Solution

Q. Let A = {1,4, 7} and B = {2, 3, 8}. Then the number of elements, in the relation R={((a1,b1),(a2b2))∈((A×B)×(A×B)) : a1+b2 divides a2+b1} is ________. [2026]

Ans. (18) Given, A = {1, 4, 7} and B = {2, 3,8} All possible sums: A/B 2 3 8 1 3 4 9 4 6 7 12 7 9 10 15 a1+b2 a2+b1 Number of pairs 15 15 1 12 12 1 10 10 1 9 9 4 7 7 1 6 6, 12 2 4 4, 12 2 3 3, 6, 9 12, 15 6 ∴ Number of relations = 18

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Q.
Let A = {1,4, 7} and B = {2, 3, 8}. Then the number of elements, in the relation $R = {((a_{1}, b_{1}), (a_{2} b_{2})) \in ((A \times B) \times (A \times B)) : a_{1} + b_{2} divides a_{2} + b_{1}}$ is ________. [2026]

Ans.
(18)

Given, A = {1, 4, 7} and B = {2, 3,8}

All possible sums:

A/B 2 3 8

1 3 4 9

4 6 7 12

7 9 10 15

$a_{1} + b_{2}$ $a_{2} + b_{1}$ Number of pairs

15 15 1

12 12 1

10 10 1

9 9 4

7 7 1

6 6, 12 2

4 4, 12 2

3 3, 6, 9 12, 15 6

$∴$ Number of relations = 18