Question

The last line in this example gives the reference to the line or lines needed for its derivation. Determine the correct rule of inference.

1. ~ P ⊃ ~ Q
2. ~ P
3. ~ Q 1, 2, ___

Answer 1

The argument uses modus tollens, a form of valid deductive reasoning, which guarantees the truth of the conclusion if the premises are true. It follows the structure of: If P then Q, Not Q, Therefore not P.

Step-by-step explanation:

The correct rule of inference used in the given argument is modus tollens. The premises provided are:

1. ~ P ⊃ ~ Q
2. ~ P

And the conclusion is:

1. ~ Q

The rule of modus tollens can be expressed in the form:

1. If P, then Q.
2. Not Q.
3. Therefore, not P.

Here, the logical structure can be seen to match modus tollens where P ⊃ Q matches the given ~ P ⊃ ~ Q, and the conclusion, ~ Q, follows from the two premises. This is an example of valid deductive reasoning, where the form of the argument guarantees that if the premises are true, the conclusion must also be true.