Exercise 1. Give the integer linear program whose value gives the independence numbeir of C, i.e., the size of the smallest independent set in a 5-cycle. Show that the fractional independence number (i.e., the optimal value of the LP without the integrality constraint) is larger than the ordinary independence number. What is the integrality gap! Exercise 1. Give the integer linear program whose value gives the independence numbeir of C, i.e., the size of the smallest independent set in a 5-cycle. Show that the fractional independence number (i.e., the optimal value of the LP without the integrality constraint) is larger than the ordinary independence number. What is the integrality gap