What is the daughter nuclide when 0-15 experiences positron emission?

The daughter isotope (a decay product)of O-15 = N-15(Nitrogen 15)

Radioactivity is the process of unstable isotopes to stable isotopes by decay, by emitting certain particles,  

O-15 emits positron particles ₁e⁰, so the atomic number decreases by 1, the mass number is the same

Reaction

The mass number of the daughter isotope = 15, atomic number = 7

If we look at the periodic system, the element with atomic number 7 is Nitrogen (N)

answer is: c. the experiment shows that the red substance experienced a chemical change.

this is chemical change (chemical reaction), because two new substances are formed (metalig liquid and gas), the atoms are rearranged and the reaction is followed by an energy change.

this is example of chemical decomposition.

chemical decomposition (analysis) is the separation of a single chemical compound into its two or more elemental parts or to simpler compounds.  

chemical decomposition is opposite of chemical synthesis.