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.

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lublana lublana · Answer 1 · 2019-09-22T11:48:39+02:00

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 :[tex]q\implies p[/tex]

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

b.Inverse :[tex]\neg p\implies \neg q[/tex]

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

c. Contrapositive:[tex]\neg q\implies \neg p[/tex]

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

d.Disjunction:p or q=[tex]p\vee q[/tex]

''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 [tex]p\wedge \neg q[/tex]

I have disease and I will not test positive.