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

{(1, 4, (2, 5), (3, 6),.....}

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{(4, 1), (5, 2), (6, 3),.....}

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{(1, 3), (2, 6), (3, 9),..}

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None of these

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Solution

The correct option is B
{(4, 1), (5, 2), (6, 3),.....}

$R = {(a, b) : a, b \in N, a - b = 3} = {((n + 3), n) : n \in N}$

={(4,1),(5,2),(6,3), .......} .

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Q. If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⇔ y = 3 x, then R =
(a) {(3, 1), (6, 2), (8, 2), (9, 3)}
(b) {(3, 1), (6, 2), (9, 3)}
(c) {(3, 1), (2, 6), (3, 9)}
(d) none of these

Q. If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is
(a) {1, 4, 6, 9}
(b) {4, 6, 9}
(c) {1}
(d) none of these

Q. The relation

R

defined in the set

{1, 2, 3, 4, 5, 6}

R = {(a, b) : b = a + 1}

Draw frequency distribution table and bar graph for the following data :

Numbers shown on the upper face of a dice thrown $50$ times :

$2, 6, 5, 1, 1, 4, 3, 2, 1, 5, 3, 3, 2, 2, 6, 6, 5, 3, 2, 1, 4, 4, 2, 1, 3, 3, 4, 2, 5, 5, 6, 6$

$3, 3, 2, 4, 5, 6, 1, 3, 3, 4, 5, 1, 2, 6, 5, 3, 2, 1 .$

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

The correct option is B {(4, 1), (5, 2), (6, 3),.....} R={(a,b):a,b∈N,a−b=3}={((n+3),n):n∈N} ={(4,1),(5,2),(6,3), .......} .

The correct option is B
{(4, 1), (5, 2), (6, 3),.....}

$R = {(a, b) : a, b \in N, a - b = 3} = {((n + 3), n) : n \in N}$

={(4,1),(5,2),(6,3), .......} .