# How do I find the equation of given Venn diagram?

How do I get the equation of given Venn diagram? What kind of steps do I want to follow ?

Example Equation: \begin{equation*} A \cap B' \cup C \end{equation*}

• As far as I know, equations are usually characterized by an equal sign. I would call this an expression instead. – Regret May 18 '15 at 8:01
• Do you mean $(A \cap B') \cup C$ or $A \cap (B' \cup C)$? That would be my first question. Because based on the figure, it's $A \cap (B' \cup C)$. – Jared May 18 '15 at 8:15

## 2 Answers

the shaded region is $A\cap C\cap B^{c}$

• if your answer is true what are the steps of getting it ? – underscore May 18 '15 at 8:06
• you look at $A\cap C$, and then subtract the part common to all sets, that's what you get. – DeepSea May 18 '15 at 8:09

As mentioned in the comments this isn't described by an equation.

We see that the area of interest is a part of A and a part of C. Furthermore the shaded area has no overlap with area B.

The area covered by two sets is called an intersection. For example let D ={1, 2, 3} and E ={3,4,5}. Then the intersection of D and E equals {3}. In your example the shaded area is completely in A and C and therefore it lies in the intersection of A and C, denoted as $A\cap C$.

However the area has no overlap with B, i.e., it has only overlap with the complement of B. We can exclude B by also taking the intersection of the complement of B, denoted by $B^c$. Then we get, as in the other aswer, $A\cap C\cap B^{c}$.