So can Venn diagrams have negative numbers because I'm stuck on a question and it's driving me crazy...I'm pretty good at math but this question has it so here it is:
$36$ employees work in a supermarket.
$24$ speak Chinese,
$20$ speak Malay
$7$ speak Tamil.
$8$ speak both Chinese and Malay,
$6$ speak both Malay and Tamil
$3$ speak both Chinese and Tamil.
Everyone speaks at least one of the $3$ languages.
Use a Venn diagram to find the number of people who speak
(a) All $3$ languages
(b) Tamil only
Please if anyone can help me on this it'll be very helpful.
So to answer it, I drew a Venn diagram. Then to find the number in Tamil I have to take the number ($7$) of people who speak Tamil and minus $6$ and $3$ but then the answer is $-2$, and I don't get it as there are $7$ people who speak tamil but $6$ who speak malay and tamil and $3$ who speak chinese and tamil...I'm stuck on that and it drives me crazy!!
Consider the diagram below.
Suppose we want to find the number of elements in the union of sets $A$, $B$, and $C$.
If we simply add the number of elements in sets $A$, $B$, and $C$, then we count each element that is in two sets twice, once for each set to which it belongs. We only want to count such elements once, so we subtract $|A \cap B| + |A \cap C| + |B \cap C|$ from $|A| + |B| + |C|$. However, if we do that we will not have counted the elements in $A \cap B \cap C$ at all since we added them three times, once for each set to which they belong, and subtracted them three times, once for each pair of sets to which they belong. Therefore, we need to add $|A \cap B \cap C|$ to the total. Doing so yields
$$|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|$$
Let $C$ be the set of employees who speak Chinese; let $M$ be the set of employees who speak Malay; let $T$ be the set of students who speak Tamil. We are given \begin{align*} |C \cup M \cup T| & = 36\\ |C| & = 24\\ |M| & = 20\\ |T| & = 7\\ |C \cap M| & = 8\\ |C \cap T| & = 3\\ |M \cap T| & = 6 \end{align*} You need to find $|C \cap M \cap T|$ and $|C^C \cap M^C \cap T|$. Can you proceed?