What is minimum required frequency of continuous time system

Question

Problem:

Question- A continuous time system, described by

y(t) = 10 Cos (2*pi*500*t) + 2 Sin (2pi*250*t)

Part 1- What is the minimum required sampling frequency?

Part 2- Write the mathematical expression that describes the discrete time (sampled) signal using the minimum required sampling frequency.

Part 3- Calculate the value of the discrete signal for n=0 and n=10

Part 4- Justify your minimum sampling frequency? Justify your answer.

Please show all the calculations step by step.