Answer
16
Work Step by Step
$A\cup B$ is the union of $A$ and $B$,
the set of all elements that are either in A or in $B$ (or in both).
$A\cap B$ is the intersection of $A$ and $B$,
the set of all elements that are common to A and $B$
Cardinality of a Union of finite sets:
$n(A\mathrm{U}B)=n(A)+n(B)-n(A\cap B)$.
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We are given
n($A\cup B)=32$
$n(A)=24$
$n(B)=48$
$n(A\cup B)=n(A)+n(B)-n(A\cap B)$
insert given values and solve for $n(A\cap B)$:
$32=24+24-n(A\cap B)$
$32=48-n(A\cap B)$
$n(A\cap B)=48-32=16$
(number of students in both A and B)
