Question

Find #(A u B u C) if #A = #B = #C = 17, #(A n B) = 5, #(B n C) = 6, #(An C) = 7, and #(A n B n C-2. You may find it helpful to draw a Venn diagram.

Answer 1

35

Explanation:

Given that A,B, C are three non empty sets.

`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`

Use the addition theory for finding no of elements in union of two or more sets

We have addition theorem as

`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)`

Now substitute for each entry from the given information

`n(AUBUC) = 17+17+17-5-6-7+2\\= 53-18\\=35`