In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea ? 

Let T denotes tea drinkers and C denotes coffee drinkers in universal set U.

From the diagram, we get 

$\begin{array}{l}a+b+c=52\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\dots \text{ (i) }\\ a=16\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\dots \text{ (ii) }\\ a+b=33\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\dots \text{ (iii) }\end{array}$

Put $a= 16$ in equation (iii), we have 

$16+b=33\Rightarrow b=17$

Now, substitute the values of a and b in

equation (i), we get

$\begin{array}{r}16+17+c=52\\ c=52-33=19\end{array}$