This is a question regarding financial mathematics on the elementary market model with two states { 1 , 2 } in a single-period. How do

This is a question regarding financial mathematics on the elementary market model with two states {ω ₁ ,ω ₂ } in a single-period. How do I show that the extended model M = (B,S,P) is arbitrage-free using the 3 conditions in FTAP that is:

There is an arbitrage opportunity if:

a) the initial wealth x=0

b) the wealth at time t=1 must be non-negative (no losses)

c) there exist any ω _i such that the wealth at time t=1 is strictly positive (there's a profit)

The P is a put option and S is a stock, B is the bond price.Here P=(P ₀ ,P ₁ ) is the price process of the put with a fixed strike K>0.