A person who is radical \((R)\) is electable \((E)\) if he/she is conservative…

Interpretation: A radical person (R) is electable (E) if and only if they are conservative (C); if they are not conservative then they are not electable. In logical terms this means: if R and C then E, and if R and not C then not E.

• Formalize the two clauses: (R ∧ C) → E and (R ∧ ¬C) → ¬E.

• Combine them to get: R → ((C → E) ∧ (¬C → ¬E)). This is equivalent to R → (E ↔ C).

Now check each given assertion against this interpretation:

• Assertion (R ∧ E) ↔ C: This is too strong because it relates C to R ∧ E even when R is false. For example, if R is false, C true and E false, the original sentence imposes no constraint but this formula would be false. Hence it is not equivalent to the intended meaning.

• Assertion R → (E ↔ C): This exactly matches the combined interpretation above, so it is correct.

• Assertion R → ((C → E) ∨ ¬E): This is too weak. Counterexample: let R = true, C = false, E = true. The assertion becomes true, but the original sentence requires that a radical non-conservative person not be electable (E false), so this formula does not capture the original meaning.

• Assertion (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E): This CNF is equivalent to the pair of implications (R ∧ E) → C and (R ∧ C) → E. For R true these force E ↔ C, so this formula is logically equivalent to R → (E ↔ C) and is therefore correct.

Conclusion: The correct assertions are the implication R → (E ↔ C) and its equivalent conjunctive normal form (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E).