Answer:
35
Step-by-step explanation:
Given that A,B, C are three non empty sets.
[tex]n(A) =n(B) =n(C) =17\\n(A \bigcap C) = 7\\n(A \bigcap B) = 5\\n(B \bigcap C) = 6\\n(A \bigcap B \bigcap C) = 7[/tex]
Use the addition theory for finding no of elements in union of two or more sets
We have addition theorem as
[tex]n(AUBUC) = n(A)+n(B)+n(C)-n(A \bigcap B)-n(B \bigcap C)-n(A \bigcap C)+n(A \bigcap B \bigcap C)[/tex]
Now substitute for each entry from the given information
[tex]n(AUBUC) = 17+17+17-5-6-7+2\\= 53-18\\=35[/tex]
