A certain city music festival set up seven categories of awards: pop, folk, rock, ethnic, electronic music, rap, and jazz. In the nomination of shortlisted names, it is known that: (1) At least 6 categories are shortlisted: (2) At least 2 categories are shortlisted among pop, folk and rock: (3) If both rock and ethnic categories are shortlisted, then electronic music and rap At least one category is not shortlisted.
Based on the above information, which of the following can be derived?
The Jazz category was not shortlisted.