$1.$Union of two non$-$convex sets cannot be convex.

$2.$ LP relaxation of Knapsack Problem cannot be solved in polynomial time.

$3.$No algorithm can provide a feasible solution for Knapsack problem in polynomial time.

$4.$Shortest path problem is an NP$-$Hard problem.

$5.$ Nearest Neighborhood Algorithm is an exact algorithm to solve TSP

$6.$ IP problems are relatively more computationally challenging problems than LP problems.