A Venn diagram has Universal set color white, set A is yellow, set B is blue, and set C is red. A intersect B is not the empty set. A intersect C is not the empty set. B intersect C is not the empty set. How many different colored including white) areas make up the Venn diagram?

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 ∩ C3. 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 ∩ CFor 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)