Let A and B be two subsets of = 1, 2, 3, -------, 44, 45 such that A = x: x is divisible by 3 and 4 B = x: x is a perfect square number Then n(B - A) equals

Step-by-step solution

The universal set is = 1, 2, 3, , 45 . The set A contains numbers divisible by both 3 and 4 , which means they are divisible by LCM (3, 4) = 12 . A = 12, 24, 36 The set B contains perfect square numbers up to 45 . B = 1^2, 2^2, 3^2, 4^2, 5^2, 6^2 = 1, 4, 9, 16, 25, 36 The set B - A contains elements that are in B but not in A . B - A = 1, 4, 9, 16, 25 Therefore, n(B - A) = 5 . Answer: 5