Final answer:
The baryon number of the Δ^{++} particle in the reaction π^+p→Δ^{++} is 1, which is conserved from the initial proton involved in the reaction.
Step-by-step explanation:
In the reaction π^+p→Δ^{++}, the baryon number of the Δ^{++} particle is conserved. Baryon number is a quantum number that represents the number of baryons (protons and neutrons) in a particle, and this number is always conserved in interactions via the strong force. Since a proton is involved in the reaction, and protons have a baryon number of 1, the Δ^{++} particle, which is created, must also have a baryon number of 1 to conserve the total baryon number in the reaction. Therefore, the correct answer is (b) 1.