Question at position 30 Either Sally is dating Charlie or Sally is dating Peter. But Sally isn't dating Charlie, because Sally won't date anyone with a tattoo, and Charlie has a large tattoo of a drunken rat on his right forearm. So, Sally is dating Peter. This argument is an argument by definitiona hypothetical argumentan argument by eliminationan inductive generalization单项选择题
A
an argument by definition
B
a hypothetical argument
C
an argument by elimination
D
an inductive generalization

Question

Question at position 30 Either Sally is dating Charlie or Sally is dating Peter. But Sally isn't dating Charlie, because Sally won't date anyone with a tattoo, and Charlie has a large tattoo of a drunken rat on his right forearm. So, Sally is dating Peter. This argument is an argument by definitiona hypothetical argumentan argument by eliminationan inductive generalization单项选择题

A

an argument by definition

B

a hypothetical argument

C

an argument by elimination

D

an inductive generalization

BlackTom AI · Accepted Answer

An argument by elimination (also called a disjunctive syllogism) has the form: “Either A or B. Not A. Therefore B.” That core form is the primary knowledge point here.

Step-by-step reasoning:
1. Identify the disjunctive premise: “Either Sally is dating Charlie or Sally is dating Peter.” This gives the disjunction A ∨ B, where A = “Sally is dating Charlie” and B = “Sally is dating Peter.”
2. Establish the negation of one disjunct: The argument supplies “Sally isn't dating Charlie,” supported by two subpremises: (i) “Sally won't date anyone with a tattoo” and (ii) “Charlie has a large tattoo.” Combining these gives ¬A (by applying the general rule to Charlie).
3. Apply the disjunctive syllogism: From A ∨ B and ¬A, infer B. Thus, conclude “Sally is dating Peter.”

Intermediate logical steps shown:
- Premise 1: A ∨ B (Either A or B).
- Premise 2a: If someone has a tattoo, Sally won't date them.
- Premise 2b: Charlie has a tattoo.
- From 2a and 2b: ¬A (Sally isn't dating Charlie).
- From A ∨ B and ¬A: therefore B (Sally is dating Peter).

Why this is correct: the argument matches exactly the disjunctive syllogism form, which is a valid deductive form known as an argument by elimination — one disjunct is eliminated (ruled out), so the remaining disjunct must obtain.

Why the other choices are incorrect:
- Argument by definition: would rely on definitional equivalence or meaning; this argument doesn’t hinge on a definition.
- A hypothetical argument (hypothetical syllogism) uses conditionals like “If P then Q”; the present structure is disjunctive, not conditional chaining.
- An inductive generalization generalizes from samples to a population; this argument makes a deductive conditional conclusion about a particular case, not a generalization.