Logic representation and reasoning $(30$ Points$)$

$($NOTE: Below we are using mathematical notation. Variables are lowercase. Constants are Uppercase.$)$

Questions:

a$.$ Translate the sentences above into First Order Logic. This will be your knowledge base.

Every runner is health conscious

Someone is health conscious if and only if that person sees the doctor regularly

Anyone who sees the doctor regularly and who has any health problem has that problem found early

Anyone who has any health problem and who has that problem found early gets that problem successfully treated

mike is a person and is a runner.

mike has the health problem diabetes.

b$.$ Translate your sentences to disjunctive form for resolution.

c$.$ Use resolution to show that diabetes problem of mike will be successfully treated.