Consider the statement: A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable. Which of these assertions are correct? (A) (R ∧ E) ⇔ C (B) R ⇒ (E ⇔ C) (C) R ⇒ ((C ⇒ E) ∨ ¬E) (D) (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E)
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Correct answer: D. (B) and (D) only
Explanation
For radicals, electable exactly when conservative: R ⇒ (E ⇔ C). Expanding gives (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E). Assertion C is a tautology, and A says something different for non-radicals.
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