Question

How many elements are in the union of four sets if the sets have 50, 60, 70, and 80 elements, respectively, each pair of the sets has 5 elements in common, each triple of the sets has 1 common element, and no element is in all four sets

Answer 1

Answer:

There are 227 elements in the union of the sets A, B, C, D.

Step-by-step explanation:

Let n(A) the number of elements of A. Then, remember that the number of elements of four set A, B, C, D is

$n(A\cup B\cup C\cup D)=n(A)+n(B)+n(C)+n(D)-n(A\cap B)-n(A\cap C)-n(A\cap D)-n(B\cap C)-n(A\cap D)-n(C\cap D)-n(A\cap B\cap C)-n(A\cap B\cap D)-n(B\cap C\cap D)-n(A\cap B\cap C \cap D)$

Then,

$n(A\cup B\cup C\cup D)=50+60+70+80-5-5-5-5-5-5-1-1-1-0=227$