Let A = {1, 2, 3, \ldots , 10} and B = { m n : m, n \in A, m < n and gcd(m, n) = 1}. Then n(B) is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for equivalence relations and set operations and simplify using the given constraints.
A = {1, 2, \ldots , 10} m (2) B{ = m, n \in A, m < n, gcd(m, n) = 1} n n(B) 1 n = 2 { } 2 1 2 n = 3 { , } 3 3 1 3 n = 4 { , } 4 4 1 2 3 4 n = 5 { , , , } 5 5 5 5 1 5 n = 6 { , } 6 6 1 2 3 4 5 6 n = 7 { , , , , , } 7 7 7 7 7 7 1 3 5 7 n = 8 { , , , } 8 8 8 8 1 2 4 5 7 8 n = 9 { , , , , , } 9 9 9 9 9 9 1 3 7 9 n = 10 { , , , } 10 10 10 10 n(B) = 31
Correct Answer: 2