In a classic Conan Doyle story, Sherlock Holmes solves a crime mystery by recognizing that a guard dog didn't bark. Therefore, the dog must have known the perpetrator. Holmes' reasoning goes like this: if the guard dog doesn't know a person, then it barks. The dog didn't bark. Therefore, it knew the person. Which rule of inference is being used here?

a. Addition.
b. Simplification.
c. Conjunction.
d. Modus Ponens.
e. Hypothetical Syllogism.
f. Disjunctive Syllogism.
g. Modus Tollens.
h. Resolution.

G. Modus tollens

Step-by-step explanation:

This question used the inference called modus tollens.

Modus tollens is a a valid form of argument that is of this form below:

If S, then T

if not S, then not T.

S = dog doesn't know perpetrator

Not S = dog knows who the perpetrator is

T = the dog barked

Not T = the dog did not bark.

So if we put this into the statement in bold letters, we would have:

The dog doesn't know perpetrator, so it barked.

And,

The dog didn't bark, so it knows the perpetrator.

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2