The relation R defined on the set of natural numbers as (a, b): a differs from b by 3 is given by

Question

The relation R defined on the set of natural numbers as (a, b): a differs from b by 3 is given by (A)  (4,1),(5,2),(6,3), ldots  (B)  (1,3),(2,6),(3,9), ldots  (C)  (1,4),(2,5),(3,6), ldots  (D) None of these

Tardigrade Admin · Accepted Answer

Given, R= (a, b): a differs from b by 3 ∵ b-a=3 ⇒ b=a+3 For, a=1, b=4 a=2, b=5 a-3, b-6 ... ... ... ... ∴ R= (1,4),(2,5),(3,6) ldots ldots

Q. The relation $R$ defined on the set of natural numbers as ${(a, b) : a$ differs from $b$ by 3 $}$ is given by

${(4, 1), (5, 2), (6, 3), \dots}$

${(1, 3), (2, 6), (3, 9), \dots}$

${(1, 4), (2, 5), (3, 6), \dots}$

None of these

Given, $R = {(a, b)$ : a differs from $b$ by 3 $}$
$∵ b - a = 3$
$\Rightarrow b = a + 3$
For, $a = 1, b = 4$
$a = 2, b = 5$
$a - 3, b - 6$
$... ...$
$... ...$
$∴ R = {(1, 4), (2, 5), (3, 6) \dots\dots}$

Q. The relation R defined on the set of natural numbers as {(a,b):a differs from b by 3} is given by

{(4,1),(5,2),(6,3),…}

{(1,3),(2,6),(3,9),…}

{(1,4),(2,5),(3,6),…}