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(A) In a ${\beta ^ + }$ decay (positron emission), a proton is converted into a neutron, a positron, and a neutrino. The process is represented as: $_

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$Z - 1$ and $A$

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(A) In a ${\beta ^ + }$ decay (positron emission), a proton is converted into a neutron, a positron, and a neutrino. The process is represented as: $_{Z}^{A}X ightarrow _{Z-1}^{A}Y + _{+1}^{0}e + 
u$.As a result, the atomic number $Z$ decreases by $1$, while the mass number $A$ remains unchanged.Subsequently, in a gamma ($\gamma$) emission, the nucleus transitions from an excited state to a lower energy state. This process does not change the atomic number $Z$ or the mass number $A$.Therefore, the final atomic number is $Z - 1$ and the final mass number is $A$.

$A$ nucleus decays by ${\beta ^ + }$ emission followed by a gamma emission. If the atomic and mass numbers of the parent nucleus are $Z$ and $A$ respectively, the corresponding numbers for the daughter nucleus are respectively.

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