MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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 βͺ B βͺ C)2. black: A β© B β© C3. yellow: A / (A β© B) βͺ (A β© C)4. blue: B / (A β© B) βͺ (B β© C)5. red: C / (B β© C) βͺ (A β© C)6. green: A β© B / (A β© B β© C)7. orange: A β© C / (A β© B β© C)8. violet: B β© C / (A β© B β© 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. Β 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 βͺ B βͺ 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 β© B β© 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 β© B) βͺ (A β© C)4. blue: B / (A β© B) βͺ (B β© C)5. red: C / (B β© C) βͺ (A β© C)Finally, for colors green, orange and violet you take the intersection of each set A β© B, A β© C and B β© C and subtract from them the elements in the black set. 6. green: A β© B / (A β© B β© C)7. orange: A β© C / (A β© B β© C)8. violet: B β© C / (A β© B β© C)