Read the following passage and solve the questions based on it.
My brother Vinit while was planning to go home last year was confused about the clothes that he should carry with him. He had the following types of clothing: belts, hats, jackets, ties, vests, T-shirts and handkerchiefs. It was also known that he had with him several pieces of each of the seven types of clothing. Finally he set up an algorithm to decide the clothes that he would be taking along with him.
(i) If he packed ties, then he did not pack handkerchiefs.
(ii) If he packed belts, then he did not pack jackets.
(iii) If he packed belts, then he packed at least one handkerchief.
(iv) If he packed jackets, then he packed at least one vest.
(v) If he packed vests, then he packed at least one handkerchief.
(vi) If he packed handkerchiefs, then he packed at least two of them.
Which one of the following statements must be false?