A European call with X$=80$ and the time to expiration $($T$)$ of $1$ year currently sells for $$10($C$0).$ The underlying stock price, S$0,$ is $$85.$ The risk$-$free interest rate is $5\%.$ You are considering purchasing a European put option with the same exercise price and expiration date.

$1)$ Does the call option price violate Fact $1?$ Explain why.

$2)$ What should be the price of the European put, P$0?$