Disjunction

1. When are the following statements true?
   The following symbols are used:
   ~ - negation,

• disjunction,
  & - conjunction,
  -> - implication

p & ~p v q
~(x v y) = ~x & ~ y
~(a -> ~b)

2. Suppose the following patient's data is in the system: age = 27, weight = 150, height = 55. Which alert will be produced by the rule below?
   IF age < 50 OR weight < 120 THEN ALERT 1 ELSE IF weight/height > 3 AND age > 27
   ALERT 2
   ELSE ALERT 3
3. Suppose that A={Diabetes, Cancer, COPD} are diagnoses for patient 1, B={Cancer, Dementia, AIDS} are diagnoses for patient 2, and C={Diabetes, Liver Disease}
   What are contents of sets: AB, AC, CB?
   For all three sets, describe in own words their meaning
4. If p(A)=0.5, p(B) = 0.25, and A and B are independent.

• what is value of p(A&B)?
• what is value of p(A|B)?