Question

How many elements are in the union of four sets if

Answer 1

Answer:

20

Step-by-step explanation:

Let A, B, C and D sets.

Let |A| the number of elements of A.

Remember, the quantity of elements that have the set $A\cup B\cup C\cup D$ is

$|A\cup B\cup C\cup D|=|A|+ |B|+ |C|+|D|-|A\cap B|-|A\cap C|-|A\cap D|-|B\cap C|-|B\cap D|-|C\cap D|-|A\cap B\cap C|-|A\cap B\cap D|-|B\cap C\cap D|-|A\cap B\cap C \cap D|$

1. Since each set has 100 elements,

2.  each pair of the sets shares 50 elements

3. each three of the sets share 25 elements,

4. the four sets share 5 elements

Then

$|A\cup B\cup C\cup D|=100+100+100+100-50-50-50-50-50-50-25-25-25-5=20$

So, there are 20 elements in the union of the sets A, B, C and D