Answer:
a) if I test positive, then I will have the disease
b) if I don't have the disease, then I won't test positive
c) if I don't test positive, then I won't have the disease
d) either I don't have the disease or I will test positive
e) I have the disease and I won't test positive.
Explanation:
Having the statement: if m, then n.
a) the converse will be:
if n, then m.
m= I have the disease
n= I (will) test positive.
converse: if I test positive, then I (will) have the disease.
(It doesn't have to be true always).
b) the inverse will be:
if not m, then not n.
inverse: if I don't have the disease, I won't test positive.
c) the contrapositive will be:
if not n, then no m.
contrapositive: if I don't test positive, then I (will) not have the disease.
(It doesn't have to be true always).
d) disjunction:
We can rewrite if m, then n as: m⇒n, the disjunction will be:
m⇒n ≡ ¬m ∨ n (not m or n).
disjunction: either I don't have the disease or I will test positive.
e) negation:
the negation of m⇒n is ¬(m⇒n) ≡ ¬(¬m ∨ n) ≡ m∧¬n.
negation: I have the disease and I won't test positive.
I have the disease but I won't test positive.
(this is the only statement completely false).