European put and call options on Intel Inc. with an exercise price of $$96$ and expiring in $90$ days are trading on the Chicago Board of Options Exchange. Intel stock is currently priced at $ $88\mathrm{.}00$ and will not make any dividend or cash payments during the life of the option. We are given that the risk free rate is $4\mathrm{.}75\%$ and that the above call option on Intel stock is priced at $$5\mathrm{.}60.$ Assume discrete compounding.

$($a$)$ Determine the fair price for the put option using the above data?

b$)$ If the market price for the put option $($on Intel$)$ is actually at $$11\mathrm{.}90,$ should we buy the option? Why or why not? Explain succinctly in a few sentences.

c$)$ Compare and Contrast Short Hedge vs$.$ Long Hedge and give one example of each strategy?