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Inverse of the Relation a=2b on Natural Numbers | JEE

JEE Maths question with a full step-by-step solution.

Question
The relation RR is defined on the set of natural numbers as {(a,b):a=2b}\{(a, b) : a = 2b\}. Then R−1R^{-1} is given by:
A{(2,1),(4,2),(6,3),…}\{(2, 1), (4, 2), (6, 3), \ldots\}
B{(1,2),(2,4),(3,6),…}\{(1, 2), (2, 4), (3, 6), \ldots\}correct
CR−1R^{-1} is not defined
DNone of these
Solution
R={(a,b):a=2b}={(2,1),(4,2),(6,3),…}.R = \{(a, b) : a = 2b\} = \{(2, 1), (4, 2), (6, 3), \ldots\}.
Reverse each pair:
R−1={(1,2),(2,4),(3,6),…}.R^{-1} = \{(1, 2), (2, 4), (3, 6), \ldots\}.
Correct answer: (2)
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