A survey of 1,000 employees in a company A survey of 1,000 employees in a company revealed that 201 like rock music, 392 like pop music, 121 like jazz, 140 like pop and rock music, 56 like jazz and rock, 37 like pop and jazz, and 18 employees like all three.
How many employees do not like jazz, pop, or rock music? 
How many employees like pop but not jazz?
 A: One could use formulas. For any set (finite) set $X$, let $|X|$ be the number of elements of $X$. You may be familiar with the formula
$$|A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|.$$
It should be fairly easy, with the information given, to figure out how many of the people like at least one of jazz, pop, or rock. The rest of the employees don't like any of these. 
It would be better if you drew a picture (Venn diagram) and reasoned things out with the aid of the picture. So draw three circles, so that any two have stuff in common, and all three have stuff in common. This should divide the world into $8$ parts (count them). Among the $8$ is the region which is outside all $3$ circles.
Look at the region of intersection of all three circles. There are $18$ people in that region. Write $18$ in that region.
There are $140$ people who like pop and rock. Among these are the $18$ people who like everything. So there are $122$ people who like pop and rock but don't like jazz. Identify the region that corresponds to the people who like pop and rock but not jazz. This is the stuff which is inside both the pop and rock circle, but outside the jazz circle. Write $122$ in this region.
Similarly, there are $56-18=38$ people who like jazz and rock but not pop. Write $38$ in that region, and then write $19$ in the region for jazz and pop but not rock.
Now look at the "pop" circle. In total, it has $201$ people. By looking at the picture, and the numbers you have, you can figure out how many of these people like pop and nothing else. Write the right number in the appropriate region. Continue. After a while, you will know the number of people in each of the $8$ regions, and now you can answer any question.  
