Omar $($single$)$ is a $50$ percent owner in Cougar LLC $($taxed as a partnership$).$ Omar works half time for Cougar and receives a guaranteed payment of $$50,000.$ Cougar LLC reported $$450,000$ of business income for the year $(2023).$ Before considering his $50$ percent business income allocation from Cougar and the self$-$employment tax deduction $($if any$),$ Omar$$s adjusted gross income is $$210,000($includes $$50,000$ guaranteed payment from Cougar and $$180,000$ salary from a different employer$).$ Omar reports itemized deductions of $$40,000.$ Answer the following questions for Omar and SHOW YOUR WORK.

a$.$ What is Omar$$s self$-$employment tax liability?

b$.$ What would be Omar$$s self$-$employment tax liability if he didn$$t receive any salary.

c$.$ What is Omar$$s net investment income tax liability $($assume no investment expenses$)?$

d$.$ What is Omar$$s additional Medicare tax liability?