Let A= x: x=4 n+1, n Z, 0 n <4 aligned & B= x: x=15 n+4, n N, n 3 & C= x: x is a prime number , x A B aligned Then the cardinal number of set C is

Step-by-step solution

The set A is defined by x = 4n + 1 for n 0, 1, 2, 3 . For n=0 , x = 4(0) + 1 = 1 . For n=1 , x = 4(1) + 1 = 5 . For n=2 , x = 4(2) + 1 = 9 . For n=3 , x = 4(3) + 1 = 13 . Thus, A = 1, 5, 9, 13 . The set B is defined by x = 15n + 4 for n 1, 2, 3 . For n=1 , x = 15(1) + 4 = 19 . For n=2 , x = 15(2) + 4 = 34 . For n=3 , x = 15(3) + 4 = 49 . Thus, B = 19, 34, 49 . The set A B = 1, 5, 9, 13, 19, 34, 49 . The set C consists of prime numbers in A B . Checking each element: 1 is not prime. 5 is prime. 9 is not prime ( 3^2