JEE Main 2024 Mathematics question
Let A = {2, 3, 6, 7} and B = {4, 5, 6, 8}. Let R be a relation defined on A × B by (a₁, b₁) R (a₂, b₂) if and only if a₁ + a₂ = b₁ + b₂. Then the number of elements in R is .......
Answer: 25
Solution
Since (a₁, b₁)R(a₂, b₂) needs a₁ + a₂ = b₁ + b₂, listing all pairs with (a₁, b₁) ≠ (a₂, b₂) gives 12 couples such as (2, 4)R(6, 4) and (2, 4)R(7, 5), each of which also holds
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