Chocolates and Venn diagrams

Statement

There is a box of chocolates. Let $A$ = milk, $\overline{A}$ = dark; $B$ = with gianduia filling, $\overline{B}$ = without filling; $C$ = spherical, $\overline{C}$ = cubic. Write the set operation that identifies:

• Red zone: the milk chocolates, spherical, without filling;
• Green zone: the dark chocolates, spherical, with gianduia filling.

Solution

Red zone — milk ($A$), spherical ($C$), without filling ($\overline{B}$): $\boxed{A\cap C\cap\overline{B}}.$

Green zone — dark ($\overline{A}$), spherical ($C$), with gianduia ($B$): $\boxed{\overline{A}\cap C\cap B}.$ The same zone can be written in a more convoluted form as $(\overline{A}\cap C)\cap(A\cup C)\cap B$: since $C\subseteq A\cup C$, the intersection with $(A\cup C)$ removes nothing and the expression simplifies to $\overline{A}\cap C\cap B$.

Links

Topics: Set theory
Concepts: Complement · Intersection · Union
Skills: Modelling
Exercise type: Word problem