Consider the following two strategies:

Strategy A: Long a call option with X₁ = $20; write two call options, each with X₂ = $30; and long a call option with X₃ = $40

Strategy B: Long a put option with X₁ = $20; write two put options, each with X₂ = $30; and long a put option with X₃ = $40

All the options have the same maturity and they are used on the same stock. Further assume that the firm pays no dividend.

Required:

Use ONLY the put-call parity to prove that both strategies A and B have the same cost. You are NOT allowed to use any other methods such as drawing terminal payoff diagram, or setting up terminal payoff table as your proof.