0
$\begingroup$

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*} enter image description here

$\endgroup$
  • 1
    $\begingroup$ As far as I know, equations are usually characterized by an equal sign. I would call this an expression instead. $\endgroup$ – Regret May 18 '15 at 8:01
  • $\begingroup$ 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 $A \cap (B' \cup C)$. $\endgroup$ – Jared May 18 '15 at 8:15
1
$\begingroup$

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

$\endgroup$
  • $\begingroup$ if your answer is true what are the steps of getting it ? $\endgroup$ – underscore May 18 '15 at 8:06
  • $\begingroup$ you look at $A\cap C$, and then subtract the part common to all sets, that's what you get. $\endgroup$ – DeepSea May 18 '15 at 8:09
1
$\begingroup$

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, $A\cap C\cap B^{c}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.