JEE Main 2024 Mathematics question
Let A = {1, 2, 3, 4, 5}. Let R be a relation on A defined by xRy if and only if 4x ≤ 5y. Let m be the number of elements in R and n be the minimum number of elements from A × A that are required to be added to R to make it a symmetric relation. Then m + n is equal to:
Answer: (C)
Solution
Counting pairs with 4x ≤ 5y gives m = 16. Nine of them have no reverse in R, so n = 9 and m + n = 25.