Let R be a relation defined on the set { 1 , 2 , 3 , 4 } { 1 , 2 , 3 , 4 } by R = { ( ( a , b ) , ( c , d ) ) : 2 a + 3 b = 3 c + 4 d } . Then the number of elements in R is [2026]

Question

Let $R$ be a relation defined on the set ${1, 2, 3, 4} \times {1, 2, 3, 4}$ by $R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d} .$

Then the number of elements in $R$ is [2026]

Smart Achievers · Accepted Answer

(4)

(a, b) (c, d)

(1, 1) x
(1, 2) x
(1, 3) (1, 2)
(1, 4) (2, 2)
(2, 1) (1, 1)
(2, 2) (2, 1)
(2, 3) (3, 1)
(2, 4) (4, 1)
(3, 1) x
(3, 2) x
(3, 3) (1, 3)
(3, 4) (2, 3)
(4, 1) (1, 2)
(4, 2) (2, 2)
(4, 3) (3, 2)
(4, 4) (4, 2)

Solution

Q.
Let $R$ be a relation defined on the set ${1, 2, 3, 4} \times {1, 2, 3, 4}$ by $R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d} .$

Then the number of elements in $R$ is [2026]

1 15

2 6

3 18

4 12

Ans.
(4)

(a, b) (c, d)

(1, 1) x
(1, 2) x
(1, 3) (1, 2)
(1, 4) (2, 2)
(2, 1) (1, 1)
(2, 2) (2, 1)
(2, 3) (3, 1)
(2, 4) (4, 1)
(3, 1) x
(3, 2) x
(3, 3) (1, 3)
(3, 4) (2, 3)
(4, 1) (1, 2)
(4, 2) (2, 2)
(4, 3) (3, 2)
(4, 4) (4, 2)

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