Final answer:
The conjectured proton decay (p → π^0 + e^+) violates both baryon number conservation and lepton number conservation. The total baryon and lepton numbers are not the same before and after the decay.
Step-by-step explanation:
The conjectured decay of the proton p → π^0 + e^+ would indeed violate both conservation of baryon number and conservation of lepton number. Baryon number conservation requires that the sum of baryon numbers before and after a reaction remains unchanged.
In this case, the proton (p) has a baryon number of +1, the pion (π^0) has a baryon number of 0, and the positron (e^+) has a baryon number of 0. The total baryon number before the decay is +1 and after the decay it would be 0, thus violating conservation of baryon number.
Similarly, lepton number conservation requires that the sum of lepton numbers remains constant through a reaction. Protons and pions have lepton numbers of 0, while the positron (e^+) has a lepton number of +1.
Given that there are no leptons on the left side of the reaction and one on the right, lepton number conservation is also violated. Therefore, the correct answer is (a) Yes, violates baryon number and lepton number conservation.