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JEE Main20262 April 2026Evening ShiftMathematicsSets and RelationsActual

Let A = 2, 3, 4, 5, 6 . Let R be a relation on the set A A given by (x, y) R (z, w) if and only if x divides z and y w . Then the number of elements in R is _______.

Correct answer

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Step-by-step solution

Given the set A = 2, 3, 4, 5, 6 . The relation R is defined on A A such that (x, y) R (z, w) if and only if x divides z and y w . The number of elements in R is the number of ordered pairs ((x, y), (z, w)) satisfying these conditions. Since the conditions for (x, z) and (y, w) are independent, the total number of elements in R will be the product of the number of pairs (x, z) satisfying x divides z and the number of pairs (y, w) satisfying y w . First, we find the number of pairs (x, z) A A such that x divides z :

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