Set P= x: x is a multiple of 4 less than 40 Q= x: x is an odd multiple of 7 less than 50 R= x: x is a multiple of 6 less than 50 Then n(P Q R)=

Step-by-step solution

The set P consists of multiples of 4 less than 40. P = 4, 8, 12, 16, 20, 24, 28, 32, 36 . Thus, n(P) = 9 . The set Q consists of odd multiples of 7 less than 50. Q = 7, 21, 35, 49 . Thus, n(Q) = 4 . The set R consists of multiples of 6 less than 50. R = 6, 12, 18, 24, 30, 36, 42, 48 . Thus, n(R) = 8 . We find the intersections: P Q = (no odd multiple of 7 is a multiple of 4). P R = 12, 24, 36 , so n(P R) = 3 . Q R = (no odd multiple of 7 is a multiple of 6). P Q R = . Using the principle of inclusion-exclusion: n(P