Question

n (U) = 692, n (A − B − C) = 30, n (B) = 470, n (B ∩ C) = 40, n (A' ∩ B' ∩ C") = 82 n (C) =?
find n(c)=?​

Answer 1

Answer:

Given n(U)=692,n(B)=230,n(C)=370,n(B∩C)=20, n(A∩B′∩C′)=10

n(A′∩B′∩C′)=n((B′∩C′)∩A′) 

n(A′∩B′∩C′)=n((B∪C)′∩A′)

=n((B∪C)′)−n((B∪C)′∩A) 

 =n(U)−n(B∪C)−n(A∩B′∩C′)

 =n(U)−n(B)−n(C)+n(B∩C)−n(A∩B′∩C′) 

=692−230−370+20−10=102