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 [tex]A\cup B\cup C\cup D[/tex] is
[tex]|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|[/tex]
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
[tex]|A\cup B\cup C\cup D|=100+100+100+100-50-50-50-50-50-50-25-25-25-5=20[/tex]
So, there are 20 elements in the union of the sets A, B, C and D
