Question

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.

Answer 1

Answer with Step-by-step explanation:

We are given that a statement ''If I have the disease , then I will test positive.''

Let p:I have the disease.

q:I will test positive.

a.Converse :
`q\implies p`

''If I will test positive, then I have the disease''.

b.Inverse :
`\\eg p\implies \\eg q`

''If I have not the disease, then I will not test positive.''

c. Contrapositive:
`\\eg q\implies \\eg p`

''If I will not test positive, then I have not the disease''.

d.Disjunction:p or q=
`p\vee q`

''I have the disease or I will test positive''.

e.Negation :If p is true then its negation is p is false.

Negation of conditional statement is equivalent to
`p\wedge \\eg q`

I have disease and I will not test positive.