(1 point) For the set S = {(x, y) : 0≤ x ≤ 1,0≤ y ≤ 1}, determine whether the following arguments are correct or incorrect: 1. The set is not convex because it is bounded. ▼ 2. The set is convex because it is compact. ▼ 3. The set is convex because it is the intersection of convex sets {(x, y) x>0} {(x, y): x <1}{(x, y) : y> 0} {(x, y): y ≤ 1}. ▼ 4. The set is convex because it is closed. ▼ 5. The set is convex because it is path-connected. 6. The set is not convex because it does not contain B(0; 1). ▼7. The set is convex because it is star-shaped, i.e. Vp Є S, Vt E [0, 1], tp = S. 8. The set is convex because Va, b = S, Vt = [0, 1], ta + (1 − t)b = S.