Avenn 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?

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)

a

step-by-step explanation: