Math And Drama Seldom Get Along

Let $n(X)$ be the number of students in a set $X$ . Also let $M$ be the set of students in the math club, $D$ the set of students in the drama club and $C$ the set of students in the whole class.

Now $n(C) = n(M \cup D) + n(\overline{M \cup D}) = (n(M) + n(D) - n(M \cap D)) + n(\overline{M \cup D}).$

But we are given that $n(M \cap D) = n(\overline{M \cup D})$ , and so

$n(C) = n(M) + n(D) = 13 + 15 = \boxed{28}$ .

Let Universal set i.e, the total number of students be $y$ .
Let number of students in both drama and math club be $x$ .
Then number of students in math club only = $(13-x)$
Then number of students in drama club only = $(15-x)$
Then number of students, who are neither in math nor drama club = $y-(15-x+13-x+x)$

According to given conditions,
$y-(15-x+13-x+x) = x$
$y-(28-x) = x$
$y-28+x = x$
$y = \boxed{28}$

In other words, the set of the number of students in math club and the set of the number of students in drama club are disjoint and together constitute the universal set.