Answer:
The Venn diagram has 8 different colored areas, in the image attached you can see the colors and the sets that make up the Venn diagram:
1. white:
U / (A ∪ B ∪ C)
2. black:
A ∩ B ∩ C
3. yellow:
A / (A ∩ B) ∪ (A ∩ C)
4. blue:
B / (A ∩ B) ∪ (B ∩ C)
5. red:
C / (B ∩ C) ∪ (A ∩ C)
6. green:
A ∩ B / (A ∩ B ∩ C)
7. orange:
A ∩ C / (A ∩ B ∩ C)
8. violet:
B ∩ C / (A ∩ B ∩ C)
Step-by-step explanation:
Each set has a color, A is yellow, B blue and C red. Taking the notation of sets and the law of combining colors, you can find all the colors that make up the diagram.
1. white: the universal set (U) has all the elements, except for those that are not in the A, B and C sets.
U / (A ∪ B ∪ C)
2. black: this color is formed with the combination of all colors in the diagram, and it contains the intersection of the 3 sets.
A ∩ B ∩ C
For colors yellow, blue and red you can take each set A, B and C and subtract from each one of them the union of the intersection of the other two sets.
3. yellow:
A / (A ∩ B) ∪ (A ∩ C)
4. blue:
B / (A ∩ B) ∪ (B ∩ C)
5. red:
C / (B ∩ C) ∪ (A ∩ C)
Finally, for colors green, orange and violet you take the intersection of each set A ∩ B, A ∩ C and B ∩ C and subtract from them the elements in the black set.
6. green:
A ∩ B / (A ∩ B ∩ C)
7. orange:
A ∩ C / (A ∩ B ∩ C)
8. violet:
B ∩ C / (A ∩ B ∩ C)
