Given the statement "if i have the disease, then i will test positive." show all work. (discrete mathematics)
a) write the converse.
b) write the inverse.
c) write the contrapositive.
d) write the statement as a disjunction.
e) write the negation.

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.

Step-by-step 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).

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

depending on others is critical to survival. my source is apex!

step-by-step explanation: