The price of a European call that expires in seven months and has a strike price of $$234$ is $$12\mathrm{.}86.$ The underlying stock price is $$231\mathrm{.}5,$ and a dividend of $$5$ is expected in four months. The risk$-$free interest rate is $4\%$ per annum $($cont$.$ comp.$).$

a$.$ What is the price of a European put option on the same stock that expires in seven months and has a strike price of $$234?$

b$.$ Let us assume some mispricing now. Show in detail the arbitrage strategies and the arbitrage profit for the following two scenarios for the European put option price in tabular form:

$1)$ Scenario $1$: The European put price is $$17\mathrm{.}40.$

$2)$ Scenario $2$: The European put price is $$11\mathrm{.}20.$

Note: Presenting the solution in a text form and not in a tabular form will attract a penalty.