Answer
In a $beta^{+}$ decay,
$P^{A}_{Z}=D^{A}_{Z-1}+e^{0}_{+1}$
so,
$Q=(m_{p}-m_{D}-m_{e})c^{2}=[{(m_{p}+Zm_{e})-[m_{D}+(Z-1)m_{e}]-2m_{e}}]c^{2}=(M_{p}-M_{D}-2m_{e})c^{2}$
Hence, proved.
Work Step by Step
In a $beta^{+}$ decay,
$P^{A}_{Z}=D^{A}_{Z-1}+e^{0}_{+1}$
so,
$Q=(m_{p}-m_{D}-m_{e})c^{2}=[{(m_{p}+Zm_{e})-[m_{D}+(Z-1)m_{e}]-2m_{e}}]c^{2}=(M_{p}-M_{D}-2m_{e})c^{2}$
Hence, proved.