For each of the statements below choose ONE of the following four options, AND ALSO explain your rationale:

• Necessary and sufficient
• Necessary but not sufficient
• Not necessary but sufficient
• Not necessary and not sufficient

Statements:

(Note: You are to assume the statements below are correct, even if you think/know they are not)

1. Hepatitis B virus is present in all Hepatitis B patients. However, some of the infected will never develop Hepatitis B and remain as silent carriers
2. Helicobacter pylori are identified in many gastric ulcer patients. Most people who test positive for H pylori have or will develop gastric ulcer
3. The unavoidable impact of collision of a fast-moving, heavy blunt object to the skull is brain hemorrhage
4. All AIDS patients are HIV positive. All individuals who have HIV will eventually develop AIDS