Let A = 1 , 3 , 4 , 6 , 9 and B = 2 , 4 , 5 , 8 , 10 . Let R be a relation defined on A × B such that R = a 1 , b 1 , a 2 , b 2 : a 1 ≤ b 2 and b 1 ≤ a 2 . Then the number of elements in the set R is

Step-by-step solution

Given, A = 1 , 3 , 4 , 6 , 9   &   B = 2 , 4 , 5 , 8 , 10 And relation is given by, R = a 1 , b 1 , a 2 , b 2 : a 1 ≤ b 2  and   b 1 ≤ a 2 Now taking cases for a 1 ≤ b 2 we get, a 1 = 1 ,   b 2 ∈ 2 , 4 , 5 , 8 , 10 → 5   cases a 1 = 3 ,   b 2 ∈ 4 , 5 , 8 , 10 → 4   cases a 1 = 4 ,   b 2 ∈ 4 , 5 , 8 , 10 → 4   cases a 1 = 6 ,   b 2 ∈ 8 , 10 → 2   cases a 1 = 9 ,   b 2 ∈ 10 &#85