Let A = 1, 4, 7 and B = 2, 3, 8 . Then the number of elements, in the relation R = ((a₁, b₁), (a₂, b₂)) ((A B) (A B)) : a₁ + b₂ divides a₂ + b₁ is _______.

Step-by-step solution

Let A = 1, 4, 7 and B = 2, 3, 8 . The relation R consists of pairs ((a₁, b₁), (a₂, b₂)) from A B such that (a₁ + b₂) divides (a₂ + b₁) . Let x = a₁ + b₂ and y = a₂ + b₁ . Note that (a₁, b₂) and (a₂, b₁) are both independent elements of A B . So choosing ((a₁, b₁), (a₂, b₂)) is equivalent to independently choosing two elements of A B with sums x and y such that x y . All possible sums a + b with a A and b B : 1 + 2 = 3 , 1 + 3 = 4 , 1 + 8 = 9 4 + 2 = 6 , 4 + 3 = 7 , 4 + 8 = 12 7 + 2 = 9 , 7 + 3 = 10 , 7 + 8 = 15 Fre