If n(A) = 2 and the number of relations from set A to set B is 1024 , then n(B) is

Step-by-step solution

Let n(A) = p and n(B) = q . The number of relations from set A to set B is given by 2^ p q . Given n(A) = 2 , we have p = 2 . The number of relations is 1024 , so 2^ 2q = 1024 . Since 1024 = 2¹⁰ , we get 2^ 2q = 2¹⁰ . Equating the exponents, 2q = 10 q = 5 . Therefore, n(B) = 5 . Answer: 5