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Consider the statement below. A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable. Few probable logical assertions of the above sentence are given below. (A) \(\left( {R \wedge E} \right) \Longleftrightarrow C\) (B) \(R\; \Rightarrow \left( {E \Leftrightarrow C} \right)\) (C) \(R \Rightarrow \left( {\left( {C \Rightarrow E} \right)V\;\neg \;E} \right)\) (D) \(\left( {\neg \;R \vee \neg \;E \vee C} \right) \wedge \left( {\neg \;R \vee \neg \;C \vee E} \right)\;\;\) Which of the above logical assertions are true? Choose the correct answer from the options given below:

Consider the statement below. A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable. Few probable logical assertions of the above sentence are given below. (A) \(\left( {R \wedge E} \right) \Longleftrightarrow C\) (B) \(R\; \Rightarrow \left( {E \Leftrightarrow C} \right)\) (C) \(R \Rightarrow \left( {\left( {C \Rightarrow E} \right)V\;\neg \;E} \right)\) (D) \(\left( {\neg \;R \vee \neg \;E \vee C} \right) \wedge \left( {\neg \;R \vee \neg \;C \vee E} \right)\;\;\) Which of the above logical assertions are true? Choose the correct answer from the options given below: Correct Answer (B) and (D) only

The correct answer is option 4

Explanation:

1) (R ∧ E) ⟺ C says that all (and only) conservatives are radical and electable. So, this assertion is not true.

2) R ⇒ (E ⇔ C) says that same as the given assertion. This is a correct assertion.

3) R ⇒ ((C ⇒ E) V ¬E) = ¬R∨(¬C∨E∨ ¬E) which is true for all interpretations. This is not a correct assertion.

4) ( ¬ R V ¬ E V C) ∧ (¬ R V ¬ C V E) = (¬ RV( E⇒ C)) ∧ (¬ R V (C ⇒ E)) = R ⇒ (E ⇔ C) which is equivalent to assertion B. This is also true.

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