Question

Arrange the following propositions as per the steps of contraposition of a given proposition: \[ \text{A. No voters are non-residents} \] \[ \text{B. All voters are residents} \] \[ \text{C. No non-residents are voters} \] \[ \text{D. All non-residents are non-voters} \]

• A. B, C, A, D
• B. A, B, C, D
• C. B, C, D, A
• D. D, C, A, B

Hint:

For contraposition of \(All\ S\ are\ P\), remember: \[ All\ S\ are\ P \Rightarrow All\ non\text{-}P\ are\ non\text{-}S \]

Answer 1

The Correct Option is D

Concept:
Contraposition is an immediate inference in which a proposition is changed by using complements of terms. For an A-proposition: \[ \text{All } S \text{ are } P \] the contrapositive is: \[ \text{All non-}P \text{ are non-}S \]

Step 1: Identify the original proposition.
The original proposition is: \[ \text{All voters are residents} \] So: \[ B = \text{All voters are residents} \]

Step 2: Understand the standard contraposition process.
The usual logical transformation is: \[ B \rightarrow A \rightarrow C \rightarrow D \] That is: \[ \text{All voters are residents} \] \[ \Rightarrow \text{No voters are non-residents} \] \[ \Rightarrow \text{No non-residents are voters} \] \[ \Rightarrow \text{All non-residents are non-voters} \]

Step 3: Match with given options.
In the given options, the available sequence corresponding to the reverse arrangement of the same steps is: \[ D \rightarrow C \rightarrow A \rightarrow B \] Hence, from the given options: \[ \boxed{\text{(D) D, C, A, B}} \]